Namespaces
namespace	projection
namespace	detail
namespace	numbers
namespace	tests

Classes
struct	AngleRadianBase
struct	AngleCartesianBase
struct	AngleFraction
struct	AxisAngleBase
class	Axis
class	AxisSigned
struct	CartesianBasis
struct	EulerBase
struct	EulerXYZBase
struct	Euler3Base
struct	QuaternionBase
struct	DualQuaternionBase
struct	AssertUnitEpsilon< QuaternionBase< U > >
struct	TypeTraits
struct	TypeTraits< float >
struct	isect_result
struct	AssertUnitEpsilon
struct	locus_entry_t

Typedefs
using	AngleRadian = AngleRadianBase<float>
using	AngleCartesian = AngleCartesianBase<float>
using	AxisAngle = AxisAngleBase<float, AngleRadianBase<float>>
using	AxisAngleCartesian = AxisAngleBase<float, AngleCartesianBase<float>>
using	EulerXYZ = EulerXYZBase<float>
using	Euler3 = Euler3Base<float>
Intermediate Types
Some functions need to have higher precision than standard floats for some operations.
using	Quaternion = QuaternionBase<float>
using	DualQuaternion = DualQuaternionBase<float>

Enumerations
enum	EulerOrder { XYZ = 1 , XZY , YXZ , YZX , ZXY , ZYX }
enum class	InterpWrapMode { Extend , Repeat , Border }
enum class	eCubicFilter { BSpline , Mitchell }

Functions
template<typename T>
T	cos (const AngleRadianBase< T > &a)
template<typename T>
T	sin (const AngleRadianBase< T > &a)
template<typename T>
T	tan (const AngleRadianBase< T > &a)
template<typename T>
T	cos (const AngleCartesianBase< T > &a)
template<typename T>
T	sin (const AngleCartesianBase< T > &a)
template<typename T>
T	tan (const AngleCartesianBase< T > &a)
template<typename T>
T	cos (const AngleFraction< T > &a)
template<typename T>
T	sin (const AngleFraction< T > &a)
template<typename T>
T	tan (const AngleFraction< T > &a)
template<typename T>
bool	is_zero (const T &a)
template<typename T>
bool	is_any_zero (const T &a)
template<typename T>
T	abs (const T &a)
template<typename T>
T	sign (const T &a)
template<typename T>
T	min (const T &a, const T &b)
template<typename T>
T	max (const T &a, const T &b)
template<typename T>
void	max_inplace (T &a, const T &b)
template<typename T>
void	min_inplace (T &a, const T &b)
template<typename T>
T	clamp (const T &a, const T &min, const T &max)
template<typename T>
T	step (const T &edge, const T &value)
template<typename T>
T	mod (const T &a, const T &b)
template<typename T>
T	safe_mod (const T &a, const T &b)
template<typename T>
T	floored_mod (const T &a, const T &b)
template<typename T>
T	safe_floored_mod (const T &a, const T &b)
template<typename T>
void	min_max (const T &value, T &min, T &max)
template<typename T>
T	safe_divide (const T &a, const T &b)
template<typename T>
T	floor (const T &a)
template<typename T>
T	round (const T &a)
template<typename T>
T	mod_periodic (const T &a, const T &b)
template<typename T>
T	ceil (const T &a)
template<typename T>
T	distance (const T &a, const T &b)
template<typename T>
T	fract (const T &a)
template<typename T>
T	sqrt (const T &a)
template<typename T>
T	rcp (const T &a)
template<typename T>
T	safe_rcp (const T &a)
template<typename T>
T	cos (const T &a)
template<typename T>
T	sin (const T &a)
template<typename T>
T	tan (const T &a)
template<typename T>
T	acos (const T &a)
template<typename T>
T	pow (const T &x, const T &power)
template<typename T>
T	safe_pow (const T &x, const T &power)
template<typename T>
T	fallback_pow (const T &x, const T &power, const T &fallback)
template<typename T>
T	square (const T &a)
template<typename T>
T	cube (const T &a)
template<typename T>
T	exp (const T &x)
template<typename T>
T	safe_acos (const T &a)
float	safe_acos_approx (float x)
template<typename T>
T	asin (const T &a)
template<typename T>
T	atan (const T &a)
template<typename T>
T	atan2 (const T &y, const T &x)
template<typename T>
T	hypot (const T &y, const T &x)
template<typename T, typename FactorT>
T	interpolate (const T &a, const T &b, const FactorT &t)
template<typename T>
T	midpoint (const T &a, const T &b)
template<eAlpha Alpha>
ColorSceneLinear4f< Alpha >	interpolate (const ColorSceneLinear4f< Alpha > &a, const ColorSceneLinear4f< Alpha > &b, const float t)
template<eAlpha Alpha>
ColorSceneLinearByteEncoded4b< Alpha >	interpolate (const ColorSceneLinearByteEncoded4b< Alpha > &a, const ColorSceneLinearByteEncoded4b< Alpha > &b, const float t)
float3	whitepoint_from_temp_tint (float temperature, float tint)
bool	whitepoint_to_temp_tint (const float3 &white, float &temperature, float &tint)
float3x3	chromatic_adaption_matrix (const float3 &from_XYZ, const float3 &to_XYZ)
std::ostream &	operator<< (std::ostream &stream, EulerOrder order)
uint16_t	float_to_half (float v)
uint16_t	float_to_half_make_finite (float v)
float	half_to_float (uint16_t v)
void	float_to_half_array (const float src, uint16_t dst, size_t length)
void	float_to_half_make_finite_array (const float src, uint16_t dst, size_t length)
void	half_to_float_array (const uint16_t src, float dst, size_t length)
void	interpolate_nearest_border_byte (const uchar buffer, uchar output, int width, int height, float u, float v)
uchar4	interpolate_nearest_border_byte (const uchar *buffer, int width, int height, float u, float v)
void	interpolate_nearest_border_fl (const float buffer, float output, int width, int height, int components, float u, float v)
float4	interpolate_nearest_border_fl (const float *buffer, int width, int height, float u, float v)
void	interpolate_nearest_byte (const uchar buffer, uchar output, int width, int height, float u, float v)
uchar4	interpolate_nearest_byte (const uchar *buffer, int width, int height, float u, float v)
void	interpolate_nearest_fl (const float buffer, float output, int width, int height, int components, float u, float v)
float4	interpolate_nearest_fl (const float *buffer, int width, int height, float u, float v)
void	interpolate_nearest_wrap_byte (const uchar buffer, uchar output, int width, int height, float u, float v)
uchar4	interpolate_nearest_wrap_byte (const uchar *buffer, int width, int height, float u, float v)
void	interpolate_nearest_wrap_fl (const float buffer, float output, int width, int height, int components, float u, float v)
float4	interpolate_nearest_wrap_fl (const float *buffer, int width, int height, float u, float v)
void	interpolate_nearest_wrapmode_fl (const float buffer, float output, int width, int height, int components, float u, float v, InterpWrapMode wrap_u, InterpWrapMode wrap_v)
uchar4	interpolate_bilinear_border_byte (const uchar *buffer, int width, int height, float u, float v)
float4	interpolate_bilinear_border_fl (const float *buffer, int width, int height, float u, float v)
void	interpolate_bilinear_border_fl (const float buffer, float output, int width, int height, int components, float u, float v)
uchar4	interpolate_bilinear_byte (const uchar *buffer, int width, int height, float u, float v)
float4	interpolate_bilinear_fl (const float *buffer, int width, int height, float u, float v)
void	interpolate_bilinear_fl (const float buffer, float output, int width, int height, int components, float u, float v)
uchar4	interpolate_bilinear_wrap_byte (const uchar *buffer, int width, int height, float u, float v)
float4	interpolate_bilinear_wrap_fl (const float *buffer, int width, int height, float u, float v)
void	interpolate_bilinear_wrapmode_fl (const float buffer, float output, int width, int height, int components, float u, float v, InterpWrapMode wrap_u, InterpWrapMode wrap_v)
uchar4	interpolate_cubic_bspline_byte (const uchar *buffer, int width, int height, float u, float v)
float4	interpolate_cubic_bspline_fl (const float *buffer, int width, int height, float u, float v)
void	interpolate_cubic_bspline_fl (const float buffer, float output, int width, int height, int components, float u, float v)
void	interpolate_cubic_bspline_wrapmode_fl (const float buffer, float output, int width, int height, int components, float u, float v, InterpWrapMode wrap_u, InterpWrapMode wrap_v)
uchar4	interpolate_cubic_mitchell_byte (const uchar *buffer, int width, int height, float u, float v)
float4	interpolate_cubic_mitchell_fl (const float *buffer, int width, int height, float u, float v)
void	interpolate_cubic_mitchell_fl (const float buffer, float output, int width, int height, int components, float u, float v)
void	transform_normals (const float3x3 &transform, MutableSpan< float3 > normals)
void	transform_normals (Span< float3 > src, const float3x3 &transform, MutableSpan< float3 > dst)
void	transform_points (const float4x4 &transform, MutableSpan< float3 > points, bool use_threading=true)
void	transform_points (Span< float3 > src, const float4x4 &transform, MutableSpan< float3 > dst, bool use_threading=true)
float3	rotate_direction_around_axis (const float3 &direction, const float3 &axis, float angle)
float3	rotate_around_axis (const float3 &vector, const float3 &center, const float3 &axis, float angle)
template<typename T, int Size>
bool	almost_equal_relative (const VecBase< T, Size > &a, const VecBase< T, Size > &b, const T &epsilon_factor)
template<typename T, int Size>
VecBase< T, Size >	abs (const VecBase< T, Size > &a)
template<typename T, int Size>
VecBase< T, Size >	sign (const VecBase< T, Size > &a)
template<typename T, int Size>
VecBase< T, Size >	min (const VecBase< T, Size > &a, const VecBase< T, Size > &b)
template<typename T, int Size>
VecBase< T, Size >	min (Span< VecBase< T, Size > > values)
template<typename T, int Size>
VecBase< T, Size >	min (std::initializer_list< VecBase< T, Size > > values)
template<typename T, int Size>
VecBase< T, Size >	max (const VecBase< T, Size > &a, const VecBase< T, Size > &b)
template<typename T, int Size>
VecBase< T, Size >	max (Span< VecBase< T, Size > > values)
template<typename T, int Size>
VecBase< T, Size >	max (std::initializer_list< VecBase< T, Size > > values)
template<typename T, int Size>
VecBase< T, Size >	clamp (const VecBase< T, Size > &a, const VecBase< T, Size > &min, const VecBase< T, Size > &max)
template<typename T, int Size>
VecBase< T, Size >	clamp (const VecBase< T, Size > &a, const T &min, const T &max)
template<typename T, int Size>
VecBase< T, Size >	step (const VecBase< T, Size > &edge, const VecBase< T, Size > &value)
template<typename T, int Size>
VecBase< T, Size >	step (const T &edge, const VecBase< T, Size > &value)
template<typename T, int Size>
VecBase< T, Size >	mod (const VecBase< T, Size > &a, const VecBase< T, Size > &b)
template<typename T, int Size>
VecBase< T, Size >	mod (const VecBase< T, Size > &a, const T &b)
template<typename T, int Size>
VecBase< T, Size >	safe_mod (const VecBase< T, Size > &a, const VecBase< T, Size > &b)
template<typename T, int Size>
VecBase< T, Size >	safe_mod (const VecBase< T, Size > &a, const T &b)
template<typename T, int Size>
VecBase< T, Size >	floored_mod (const VecBase< T, Size > &a, const VecBase< T, Size > &b)
template<typename T, int Size>
VecBase< T, Size >	floored_mod (const VecBase< T, Size > &a, const T &b)
template<typename T, int Size>
VecBase< T, Size >	pow (const VecBase< T, Size > &x, const T &y)
template<typename T, int Size>
VecBase< T, Size >	safe_pow (const VecBase< T, Size > &x, const T &y)
template<typename T, int Size>
VecBase< T, Size >	fallback_pow (const VecBase< T, Size > &x, const T &y, const VecBase< T, Size > &fallback)
template<typename T, int Size>
VecBase< T, Size >	pow (const VecBase< T, Size > &x, const VecBase< T, Size > &y)
template<typename T, int Size>
VecBase< T, Size >	square (const VecBase< T, Size > &a)
template<typename T, int Size>
VecBase< T, Size >	exp (const VecBase< T, Size > &x)
template<typename T, int Size>
VecBase< T, Size >	ceil_to_multiple (const VecBase< T, Size > &a, const VecBase< T, Size > &b)
template<typename T, int Size>
VecBase< T, Size >	divide_ceil (const VecBase< T, Size > &a, const VecBase< T, Size > &b)
template<typename T, int Size>
void	min_max (const VecBase< T, Size > &vector, VecBase< T, Size > &min, VecBase< T, Size > &max)
template<typename T, int Size>
VecBase< T, Size >	safe_divide (const VecBase< T, Size > &a, const VecBase< T, Size > &b)
template<typename T, int Size>
VecBase< T, Size >	safe_divide (const VecBase< T, Size > &a, const T &b)
template<typename T, int Size>
VecBase< T, Size >	floor (const VecBase< T, Size > &a)
template<typename T, int Size>
VecBase< T, Size >	round (const VecBase< T, Size > &a)
template<typename T, int Size>
VecBase< T, Size >	ceil (const VecBase< T, Size > &a)
template<typename T, int Size>
VecBase< T, Size >	sqrt (const VecBase< T, Size > &a)
template<typename T, int Size>
VecBase< T, Size >	safe_sqrt (const VecBase< T, Size > &a)
template<typename T, int Size>
VecBase< T, Size >	rcp (const VecBase< T, Size > &a)
template<typename T, int Size>
VecBase< T, Size >	safe_rcp (const VecBase< T, Size > &a)
template<typename T, int Size>
VecBase< T, Size >	fract (const VecBase< T, Size > &a)
template<typename T, int Size>
T	dot (const VecBase< T, Size > &a, const VecBase< T, Size > &b)
template<typename T, int Size>
T	length_manhattan (const VecBase< T, Size > &a)
template<typename T, int Size>
T	length_squared (const VecBase< T, Size > &a)
template<typename T, int Size>
T	length (const VecBase< T, Size > &a)
template<typename T, int Size>
bool	is_unit_scale (const VecBase< T, Size > &v)
template<typename T, int Size>
T	distance_manhattan (const VecBase< T, Size > &a, const VecBase< T, Size > &b)
template<typename T, int Size>
T	distance_squared (const VecBase< T, Size > &a, const VecBase< T, Size > &b)
template<typename T, int Size>
T	distance (const VecBase< T, Size > &a, const VecBase< T, Size > &b)
template<typename T, int Size>
VecBase< T, Size >	reflect (const VecBase< T, Size > &incident, const VecBase< T, Size > &normal)
template<typename T, int Size>
VecBase< T, Size >	refract (const VecBase< T, Size > &incident, const VecBase< T, Size > &normal, const T &eta)
template<typename T, int Size>
VecBase< T, Size >	project (const VecBase< T, Size > &p, const VecBase< T, Size > &v_proj)
template<typename T, int Size>
VecBase< T, Size >	normalize_and_get_length (const VecBase< T, Size > &v, T &out_length)
template<typename T, int Size>
VecBase< T, Size >	normalize (const VecBase< T, Size > &v)
template<typename T>
T	cross (const VecBase< T, 2 > &a, const VecBase< T, 2 > &b)
template<typename T>
VecBase< T, 3 >	cross (const VecBase< T, 3 > &a, const VecBase< T, 3 > &b)
VecBase< float, 3 >	cross_high_precision (const VecBase< float, 3 > &a, const VecBase< float, 3 > &b)
template<typename T>
VecBase< T, 3 >	cross_poly (Span< VecBase< T, 3 > > poly)
template<typename T>
VecBase< T, 3 >	cross_tri (const VecBase< T, 3 > &v1, const VecBase< T, 3 > &v2, const VecBase< T, 3 > &v3)
template<typename T>
VecBase< T, 3 >	normal_tri (const VecBase< T, 3 > &v1, const VecBase< T, 3 > &v2, const VecBase< T, 3 > &v3)
template<typename T, typename FactorT, int Size>
VecBase< T, Size >	interpolate (const VecBase< T, Size > &a, const VecBase< T, Size > &b, const FactorT &t)
template<typename T, int Size>
VecBase< T, Size >	midpoint (const VecBase< T, Size > &a, const VecBase< T, Size > &b)
template<typename T, int Size>
VecBase< T, Size >	faceforward (const VecBase< T, Size > &vector, const VecBase< T, Size > &incident, const VecBase< T, Size > &reference)
template<typename T>
int	dominant_axis (const VecBase< T, 3 > &a)
template<typename T, int Size>
T	reduce_max (const VecBase< T, Size > &a)
template<typename T, int Size>
T	reduce_min (const VecBase< T, Size > &a)
template<typename T, int Size>
T	reduce_add (const VecBase< T, Size > &a)
template<typename T, int Size>
T	reduce_mul (const VecBase< T, Size > &a)
template<typename T, int Size>
T	average (const VecBase< T, Size > &a)
template<typename T>
VecBase< T, 3 >	orthogonal (const VecBase< T, 3 > &v)
template<typename T>
VecBase< T, 2 >	orthogonal (const VecBase< T, 2 > &v)
template<typename T, int Size>
bool	is_equal (const VecBase< T, Size > &a, const VecBase< T, Size > &b, const T epsilon=T(0))
template<typename T, int Size>
bool	is_zero (const VecBase< T, Size > &a, const T epsilon=T(0))
template<typename T, int Size>
bool	is_any_zero (const VecBase< T, Size > &a)
template<typename T, int Size>
bool	is_unit (const VecBase< T, Size > &a, const T epsilon=T(10) *std::numeric_limits< T >::epsilon())
template<typename T, int Size>
isect_result< VecBase< T, Size > >	isect_seg_seg (const VecBase< T, Size > &v1, const VecBase< T, Size > &v2, const VecBase< T, Size > &v3, const VecBase< T, Size > &v4)
template<typename T>
uint64_t	vector_hash (const T &vec)
std::ostream &	operator<< (std::ostream &stream, const Axis axis)
std::ostream &	operator<< (std::ostream &stream, const AxisSigned axis)
std::ostream &	operator<< (std::ostream &stream, const CartesianBasis &rot)
BLI_INLINE int	wrap_coord (float u, int size, InterpWrapMode wrap)
template<enum eCubicFilter filter>
static float4	cubic_filter_coefficients (float f)
template<typename T, eCubicFilter filter>
BLI_INLINE void	bicubic_interpolation (const T src_buffer, T output, int width, int height, int components, float u, float v, InterpWrapMode wrap_u, InterpWrapMode wrap_v)
BLI_INLINE void	bilinear_fl_impl (const float buffer, float output, int width, int height, int components, float u, float v, InterpWrapMode wrap_x, InterpWrapMode wrap_y)
template<bool border>
BLI_INLINE uchar4	bilinear_byte_impl (const uchar *buffer, int width, int height, float u, float v)
template<typename T>
bool	is_similarity_transform (const MatBase< T, 3, 3 > &matrix, const T &epsilon=1e-6)
static bool	skip_transform (const float4x4 &transform)
static void	transform_points_no_threading (const Span< float3 > src, const float4x4 &transform, MutableSpan< float3 > dst)
static void	transform_points_no_threading (const float4x4 &transform, MutableSpan< float3 > points)
template<>
isect_result< float2 >	isect_seg_seg (const float2 &v1, const float2 &v2, const float2 &v3, const float2 &v4)
template<>
isect_result< double2 >	isect_seg_seg (const double2 &v1, const double2 &v2, const double2 &v3, const double2 &v4)
Conversion to Quaternions
template<typename T, typename AngleT>
QuaternionBase< T >	to_quaternion (const AxisAngleBase< T, AngleT > &axis_angle)
template<typename T>
QuaternionBase< T >	to_quaternion (const EulerXYZBase< T > &eul)
template<typename T>
QuaternionBase< T >	to_quaternion (const Euler3Base< T > &eulO)
Conversion to Euler
template<typename T, typename AngleT>
Euler3Base< T >	to_euler (const AxisAngleBase< T, AngleT > &axis_angle, EulerOrder order)
template<typename T, typename AngleT>
EulerXYZBase< T >	to_euler (const AxisAngleBase< T, AngleT > &axis_angle)
template<typename T, typename AngleT = AngleRadian>
AxisAngleBase< T, AngleT >	to_axis_angle (const QuaternionBase< T > &quat)
template<typename T>
EulerXYZBase< T >	to_euler (const QuaternionBase< T > &quat)
template<typename T>
Euler3Base< T >	to_euler (const QuaternionBase< T > &quat, EulerOrder order)
Axes
constexpr bool	operator<= (const Axis::Value a, const Axis::Value b)
constexpr bool	operator<= (const AxisSigned::Value a, const AxisSigned::Value b)
Axes Utilities
template<>
AxisSigned	abs (const AxisSigned &axis)
int	sign (const AxisSigned &axis)
AxisSigned	cross (const AxisSigned a, const AxisSigned b)
template<typename T>
T	to_vector (const Axis axis)
template<typename T>
T	to_vector (const AxisSigned axis)
CartesianBasis
CartesianBasis	from_orthonormal_axes (const AxisSigned forward, const AxisSigned up)
CartesianBasis	rotation_between (const CartesianBasis &a, const CartesianBasis &b)
CartesianBasis	rotation_between (const AxisSigned a_forward, const AxisSigned b_forward)
template<typename T>
VecBase< T, 3 >	transform_point (const CartesianBasis &basis, const VecBase< T, 3 > &v)
CartesianBasis	invert (const CartesianBasis &basis)
Conversion to axis angles
template<typename T, typename AngleT = AngleRadian>
AxisAngleBase< T, AngleT >	to_axis_angle (const EulerXYZBase< T > &euler)
template<typename T, typename AngleT = AngleRadian>
AxisAngleBase< T, AngleT >	to_axis_angle (const Euler3Base< T > &euler)
Matrix Operations
template<typename T, int Size>
MatBase< T, Size, Size >	invert (const MatBase< T, Size, Size > &mat, bool &r_success)
template<typename T, int NumCol, int NumRow>
MatBase< T, NumCol, NumRow >	transpose (const MatBase< T, NumRow, NumCol > &mat)
template<typename T, int NumCol, int NumRow>
MatBase< T, NumCol, NumRow >	normalize (const MatBase< T, NumCol, NumRow > &a)
template<typename T, int NumCol, int NumRow, typename VectorT>
MatBase< T, NumCol, NumRow >	normalize_and_get_size (const MatBase< T, NumCol, NumRow > &a, VectorT &r_size)
template<typename T, int Size>
T	determinant (const MatBase< T, Size, Size > &mat)
template<typename T, int Size>
MatBase< T, Size, Size >	adjoint (const MatBase< T, Size, Size > &mat)
template<typename T, int NumCol, int NumRow, typename VectorT>
MatBase< T, NumCol, NumRow >	translate (const MatBase< T, NumCol, NumRow > &mat, const VectorT &translation)
template<typename T, int NumCol, int NumRow, typename RotationT>
MatBase< T, NumCol, NumRow >	rotate (const MatBase< T, NumCol, NumRow > &mat, const RotationT &rotation)
template<typename T, int NumCol, int NumRow, typename VectorT>
MatBase< T, NumCol, NumRow >	scale (const MatBase< T, NumCol, NumRow > &mat, const VectorT &scale)
template<typename T, int NumCol, int NumRow>
MatBase< T, NumCol, NumRow >	interpolate_linear (const MatBase< T, NumCol, NumRow > &a, const MatBase< T, NumCol, NumRow > &b, T t)
template<typename T>
MatBase< T, 3, 3 >	interpolate (const MatBase< T, 3, 3 > &a, const MatBase< T, 3, 3 > &b, T t)
template<typename T>
MatBase< T, 4, 4 >	interpolate (const MatBase< T, 4, 4 > &a, const MatBase< T, 4, 4 > &b, T t)
template<typename T>
MatBase< T, 3, 3 >	interpolate_fast (const MatBase< T, 3, 3 > &a, const MatBase< T, 3, 3 > &b, T t)
template<typename T>
MatBase< T, 4, 4 >	interpolate_fast (const MatBase< T, 4, 4 > &a, const MatBase< T, 4, 4 > &b, T t)
template<typename T, int Size>
MatBase< T, Size, Size >	pseudo_invert (const MatBase< T, Size, Size > &mat, T epsilon=1e-8)
Init helpers.
template<typename MatT>
MatT	from_location (const typename MatT::loc_type &location)
template<typename MatT, int ScaleDim>
MatT	from_scale (const VecBase< typename MatT::base_type, ScaleDim > &scale)
template<typename MatT, typename RotationT>
MatT	from_rotation (const RotationT &rotation)
template<typename MatT, typename RotationT, typename VectorT>
MatT	from_rot_scale (const RotationT &rotation, const VectorT &scale)
template<typename MatT, typename RotationT>
MatT	from_loc_rot (const typename MatT::loc_type &location, const RotationT &rotation)
template<typename MatT, int ScaleDim>
MatT	from_loc_scale (const typename MatT::loc_type &location, const VecBase< typename MatT::base_type, ScaleDim > &scale)
template<typename MatT, typename RotationT, int ScaleDim>
MatT	from_loc_rot_scale (const typename MatT::loc_type &location, const RotationT &rotation, const VecBase< typename MatT::base_type, ScaleDim > &scale)
template<typename T>
MatBase< T, 2, 2 >	from_direction (const VecBase< T, 2 > &direction)
template<typename MatT, typename VectorT>
MatT	from_orthonormal_axes (const VectorT forward, const VectorT up)
template<typename MatT, typename VectorT>
MatT	from_orthonormal_axes (const VectorT location, const VectorT forward, const VectorT up)
template<typename MatT, typename VectorT>
MatT	from_up_axis (const VectorT up)
template<typename MatT>
MatT	orthogonalize (const MatT &mat, const Axis axis)
template<typename MatT, typename VectorT>
MatT	from_origin_transform (const MatT &transform, const VectorT origin)
Conversion function.
template<typename T>
AngleRadianBase< T >	to_angle (const MatBase< T, 2, 2 > &mat)
template<typename T>
EulerXYZBase< T >	to_euler (const MatBase< T, 3, 3 > &mat)
template<typename T>
EulerXYZBase< T >	to_euler (const MatBase< T, 4, 4 > &mat)
template<typename T>
Euler3Base< T >	to_euler (const MatBase< T, 3, 3 > &mat, EulerOrder order)
template<typename T>
Euler3Base< T >	to_euler (const MatBase< T, 4, 4 > &mat, EulerOrder order)
template<typename T>
EulerXYZBase< T >	to_nearest_euler (const MatBase< T, 3, 3 > &mat, const EulerXYZBase< T > &reference)
template<typename T>
EulerXYZBase< T >	to_nearest_euler (const MatBase< T, 4, 4 > &mat, const EulerXYZBase< T > &reference)
template<typename T>
Euler3Base< T >	to_nearest_euler (const MatBase< T, 3, 3 > &mat, const Euler3Base< T > &reference)
template<typename T>
Euler3Base< T >	to_nearest_euler (const MatBase< T, 4, 4 > &mat, const Euler3Base< T > &reference)
template<typename T>
QuaternionBase< T >	to_quaternion (const MatBase< T, 3, 3 > &mat)
template<typename T>
QuaternionBase< T >	to_quaternion (const MatBase< T, 4, 4 > &mat)
Quaternion	to_quaternion_legacy (const float3x3 &mat)
template<bool AllowNegativeScale = false, typename T, int NumCol, int NumRow>
VecBase< T, 3 >	to_scale (const MatBase< T, NumCol, NumRow > &mat)
template<bool AllowNegativeScale = false, typename T>
VecBase< T, 2 >	to_scale (const MatBase< T, 2, 2 > &mat)
template<bool AllowNegativeScale = false, typename T>
void	to_rot_scale (const MatBase< T, 2, 2 > &mat, AngleRadianBase< T > &r_rotation, VecBase< T, 2 > &r_scale)
template<bool AllowNegativeScale = false, typename T>
void	to_loc_rot_scale (const MatBase< T, 3, 3 > &mat, VecBase< T, 2 > &r_location, AngleRadianBase< T > &r_rotation, VecBase< T, 2 > &r_scale)
template<bool AllowNegativeScale = false, typename T, typename RotationT>
void	to_rot_scale (const MatBase< T, 3, 3 > &mat, RotationT &r_rotation, VecBase< T, 3 > &r_scale)
template<bool AllowNegativeScale = false, typename T, typename RotationT>
void	to_loc_rot_scale (const MatBase< T, 4, 4 > &mat, VecBase< T, 3 > &r_location, RotationT &r_rotation, VecBase< T, 3 > &r_scale)
Transform functions.
template<typename T>
VecBase< T, 2 >	transform_point (const MatBase< T, 2, 2 > &mat, const VecBase< T, 2 > &point)
template<typename T>
VecBase< T, 2 >	transform_point (const MatBase< T, 3, 3 > &mat, const VecBase< T, 2 > &point)
template<typename T>
VecBase< T, 3 >	transform_point (const MatBase< T, 3, 3 > &mat, const VecBase< T, 3 > &point)
template<typename T>
VecBase< T, 3 >	transform_point (const MatBase< T, 4, 4 > &mat, const VecBase< T, 3 > &point)
template<typename T>
VecBase< T, 3 >	transform_direction (const MatBase< T, 3, 3 > &mat, const VecBase< T, 3 > &direction)
template<typename T>
VecBase< T, 3 >	transform_direction (const MatBase< T, 4, 4 > &mat, const VecBase< T, 3 > &direction)
template<typename MatT, typename VectorT>
VectorT	project_point (const MatT &mat, const VectorT &point)
template<typename T>
VecBase< T, 3 >	transform_point (const QuaternionBase< T > &q, const VecBase< T, 3 > &v)
Compare / Test
template<typename T>
bool	is_negative (const MatBase< T, 3, 3 > &mat)
template<typename T>
bool	is_negative (const MatBase< T, 4, 4 > &mat)
template<typename T, int NumCol, int NumRow>
bool	is_equal (const MatBase< T, NumCol, NumRow > &a, const MatBase< T, NumCol, NumRow > &b, const T epsilon=T(0))
template<typename T, int NumCol, int NumRow>
bool	is_identity (const MatBase< T, NumCol, NumRow > &mat)
template<typename MatT>
bool	is_orthogonal (const MatT &mat)
template<typename MatT>
bool	is_orthonormal (const MatT &mat)
template<typename MatT>
bool	is_uniformly_scaled (const MatT &mat)
template<typename T, int NumCol, int NumRow>
bool	is_zero (const MatBase< T, NumCol, NumRow > &mat)
Implementation.
template<typename T, int NumCol, int NumRow>
bool	is_unit_scale (const MatBase< T, NumCol, NumRow > &m)
template<typename T, int Size>
MatBase< T, Size, Size >	invert (const MatBase< T, Size, Size > &mat)
template<typename T, int NumCol, int NumRow, typename AngleT>
MatBase< T, NumCol, NumRow >	rotate (const MatBase< T, NumCol, NumRow > &mat, const AxisAngleBase< T, AngleT > &rotation)
template<typename T, int NumCol, int NumRow, int SrcNumCol, int SrcNumRow, int SrcStartCol, int SrcStartRow, int SrcAlignment>
MatBase< T, NumCol, NumRow >	normalize (const MatView< T, NumCol, NumRow, SrcNumCol, SrcNumRow, SrcStartCol, SrcStartRow, SrcAlignment > &a)
template<typename T, int NumCol, int NumRow, int SrcNumCol, int SrcNumRow, int SrcStartCol, int SrcStartRow, int SrcAlignment, typename VectorT>
MatBase< T, NumCol, NumRow >	normalize_and_get_size (const MatView< T, NumCol, NumRow, SrcNumCol, SrcNumRow, SrcStartCol, SrcStartRow, SrcAlignment > &a, VectorT &r_size)
template<typename T>
QuaternionBase< T >	normalized_to_quaternion_safe (const MatBase< T, 3, 3 > &mat)
template<bool AllowNegativeScale, typename T, typename RotationT>
void	to_loc_rot_scale_safe (const MatBase< T, 4, 4 > &mat, VecBase< T, 3 > &r_location, RotationT &r_rotation, VecBase< T, 3 > &r_scale)
template<typename T, int N, int NumRow>
VecBase< T, N >	project_point (const MatBase< T, N+1, NumRow > &mat, const VecBase< T, N > &point)
template float3	transform_point (const float3x3 &mat, const float3 &point)
template float3	transform_point (const float4x4 &mat, const float3 &point)
template float3	transform_direction (const float3x3 &mat, const float3 &direction)
template float3	transform_direction (const float4x4 &mat, const float3 &direction)
template float3	project_point (const float4x4 &mat, const float3 &point)
template float2	project_point (const float3x3 &mat, const float2 &point)
Quaternion functions.
template<typename T>
T	dot (const QuaternionBase< T > &a, const QuaternionBase< T > &b)
template<typename T>
QuaternionBase< T >	pow (const QuaternionBase< T > &q, const T &y)
template<typename T>
QuaternionBase< T >	conjugate (const QuaternionBase< T > &a)
template<typename T>
QuaternionBase< T >	canonicalize (const QuaternionBase< T > &q)
template<typename T>
QuaternionBase< T >	invert (const QuaternionBase< T > &q)
template<typename T>
QuaternionBase< T >	invert_normalized (const QuaternionBase< T > &q)
template<typename T>
QuaternionBase< T >	normalize (const QuaternionBase< T > &q)
template<typename T>
QuaternionBase< T >	normalize_and_get_length (const QuaternionBase< T > &q, T &out_length)
template<typename T>
QuaternionBase< T >	interpolate (const QuaternionBase< T > &a, const QuaternionBase< T > &b, T t)
Test functions.
template<typename T>
bool	is_zero (const QuaternionBase< T > &q)
template<typename T>
bool	is_equal (const QuaternionBase< T > &a, const QuaternionBase< T > &b, const T epsilon=T(0))
template<typename T>
bool	is_unit_scale (const QuaternionBase< T > &q)
Quaternion
template<typename T>
VecBase< T, 2 >	interpolate_dot_slerp (const T t, const T cosom)
Dual-Quaternion
template<typename T>
DualQuaternionBase< T >	normalize (const DualQuaternionBase< T > &dual_quat)
template<typename T>
VecBase< T, 3 >	transform_point (const DualQuaternionBase< T > &dq, const VecBase< T, 3 > &point, MatBase< T, 3, 3 > *r_crazy_space_mat=nullptr)
template<typename T>
DualQuaternionBase< T >	to_dual_quaternion (const MatBase< T, 4, 4 > &mat, const MatBase< T, 4, 4 > &basemat)
template<typename T>
bool	is_normalized (const DualQuaternionBase< T > &dq)
Rotation helpers
template<typename T, typename RotT>
QuaternionBase< T >	rotate (const QuaternionBase< T > &a, const RotT &b)
template<typename T, typename RotT, typename AngleT>
AxisAngleBase< T, AngleT >	rotate (const AxisAngleBase< T, AngleT > &a, const RotT &b)
template<typename T, typename RotT>
EulerXYZBase< T >	rotate (const EulerXYZBase< T > &a, const RotT &b)
template<typename T, typename RotT>
Euler3Base< T >	rotate (const Euler3Base< T > &a, const RotT &b)
template<typename T>
QuaternionBase< T >	rotation_between (const QuaternionBase< T > &a, const QuaternionBase< T > &b)
template<typename T>
QuaternionBase< T >	from_triangle (const VecBase< T, 3 > &v1, const VecBase< T, 3 > &v2, const VecBase< T, 3 > &v3, const VecBase< T, 3 > &normal)
template<typename T>
QuaternionBase< T >	from_triangle (const VecBase< T, 3 > &v1, const VecBase< T, 3 > &v2, const VecBase< T, 3 > &v3)
template<typename T>
QuaternionBase< T >	from_vector (const VecBase< T, 3 > &vector, const AxisSigned track_flag, const Axis up_flag)
template<typename T>
QuaternionBase< T >	from_tracking (AxisSigned forward_axis, Axis up_axis)
template<typename T>
MatBase< T, 3, 3 >	to_gimbal_axis (const Euler3Base< T > &rotation)
Angles
template<typename T>
AngleRadianBase< T >	angle_of (const QuaternionBase< T > &q)
template<typename T>
AngleRadianBase< T >	angle_of_signed (const QuaternionBase< T > &q)
template<typename T>
AngleRadianBase< T >	angle_between (const QuaternionBase< T > &a, const QuaternionBase< T > &b)
template<typename T>
AngleRadianBase< T >	angle_between (const VecBase< T, 3 > &a, const VecBase< T, 3 > &b)
template<typename T>
AngleFraction< T >	angle_between (const AxisSigned a, const AxisSigned b)
template<typename T>
AngleRadianBase< T >	angle_between_signed (const QuaternionBase< T > &a, const QuaternionBase< T > &b)
Conversion from Cartesian Basis
template<typename T>
QuaternionBase< T >	to_quaternion (const CartesianBasis &rotation)
Explicit Template Instantiations
template EulerXYZ	to_euler (const AxisAngle &)
template EulerXYZ	to_euler (const AxisAngleCartesian &)
template EulerXYZ	to_euler (const Quaternion &)
template Euler3	to_euler (const AxisAngle &, EulerOrder)
template Euler3	to_euler (const AxisAngleCartesian &, EulerOrder)
template Euler3	to_euler (const Quaternion &, EulerOrder)
template Quaternion	to_quaternion (const AxisAngle &)
template Quaternion	to_quaternion (const AxisAngleCartesian &)
template Quaternion	to_quaternion (const Euler3 &)
template Quaternion	to_quaternion (const EulerXYZ &)
template AxisAngleCartesian	to_axis_angle (const Euler3 &)
template AxisAngleCartesian	to_axis_angle (const EulerXYZ &)
template AxisAngleCartesian	to_axis_angle (const Quaternion &)
Determinant
template float	determinant (const float2x2 &mat)
template float	determinant (const float3x3 &mat)
template float	determinant (const float4x4 &mat)
template double	determinant (const double2x2 &mat)
template double	determinant (const double3x3 &mat)
template double	determinant (const double4x4 &mat)
template bool	is_negative (const float3x3 &mat)
template bool	is_negative (const float4x4 &mat)
template bool	is_negative (const double3x3 &mat)
template bool	is_negative (const double4x4 &mat)
Adjoint
template float2x2	adjoint (const float2x2 &mat)
template float3x3	adjoint (const float3x3 &mat)
template float4x4	adjoint (const float4x4 &mat)
template double2x2	adjoint (const double2x2 &mat)
template double3x3	adjoint (const double3x3 &mat)
template double4x4	adjoint (const double4x4 &mat)
Inverse
template float2x2	invert (const float2x2 &mat, bool &r_success)
template float3x3	invert (const float3x3 &mat, bool &r_success)
template float4x4	invert (const float4x4 &mat, bool &r_success)
template double2x2	invert (const double2x2 &mat, bool &r_success)
template double3x3	invert (const double3x3 &mat, bool &r_success)
template double4x4	invert (const double4x4 &mat, bool &r_success)
template float2x2	pseudo_invert (const float2x2 &mat, float epsilon)
template float3x3	pseudo_invert (const float3x3 &mat, float epsilon)
template float4x4	pseudo_invert (const float4x4 &mat, float epsilon)
template double2x2	pseudo_invert (const double2x2 &mat, double epsilon)
template double3x3	pseudo_invert (const double3x3 &mat, double epsilon)
template double4x4	pseudo_invert (const double4x4 &mat, double epsilon)
Polar Decomposition
template<typename T>
static void	polar_decompose (const MatBase< T, 3, 3 > &mat3, MatBase< T, 3, 3 > &r_U, MatBase< T, 3, 3 > &r_P)
Interpolate
template float3x3	interpolate (const float3x3 &a, const float3x3 &b, float t)
template double3x3	interpolate (const double3x3 &a, const double3x3 &b, double t)
template float4x4	interpolate (const float4x4 &a, const float4x4 &b, float t)
template double4x4	interpolate (const double4x4 &a, const double4x4 &b, double t)
template float3x3	interpolate_fast (const float3x3 &a, const float3x3 &b, float t)
template double3x3	interpolate_fast (const double3x3 &a, const double3x3 &b, double t)
template float4x4	interpolate_fast (const float4x4 &a, const float4x4 &b, float t)
template double4x4	interpolate_fast (const double4x4 &a, const double4x4 &b, double t)

Variables
template<typename T>
constexpr bool	is_math_float_type = std::is_floating_point_v<T>
template<typename T>
constexpr bool	is_math_integral_type = std::is_integral_v<T>
static const std::array< locus_entry_t, 31 >	planck_locus

Typedef Documentation

◆ AngleCartesian

using blender::math::AngleCartesian = AngleCartesianBase<float>

Definition at line 724 of file BLI_math_angle_types.hh.

◆ AngleRadian

using blender::math::AngleRadian = AngleRadianBase<float>

Definition at line 723 of file BLI_math_angle_types.hh.

◆ AxisAngle

using blender::math::AxisAngle = AxisAngleBase<float, AngleRadianBase<float>>

Definition at line 89 of file BLI_math_axis_angle_types.hh.

◆ AxisAngleCartesian

using blender::math::AxisAngleCartesian = AxisAngleBase<float, AngleCartesianBase<float>>

Definition at line 90 of file BLI_math_axis_angle_types.hh.

◆ DualQuaternion

using blender::math::DualQuaternion = DualQuaternionBase<float>

Definition at line 317 of file BLI_math_quaternion_types.hh.

◆ Euler3

using blender::math::Euler3 = Euler3Base<float>

Definition at line 436 of file BLI_math_euler_types.hh.

◆ EulerXYZ

using blender::math::EulerXYZ = EulerXYZBase<float>

Definition at line 435 of file BLI_math_euler_types.hh.

◆ Quaternion

using blender::math::Quaternion = QuaternionBase<float>

Definition at line 316 of file BLI_math_quaternion_types.hh.

Enumeration Type Documentation

◆ eCubicFilter

enum class blender::math::eCubicFilter

strong

Enumerator
BSpline
Mitchell

Definition at line 69 of file math_interp.cc.

◆ EulerOrder

enum blender::math::EulerOrder

Enumerator
XYZ
XZY
YXZ
YZX
ZXY
ZYX

Definition at line 40 of file BLI_math_euler_types.hh.

◆ InterpWrapMode

enum class blender::math::InterpWrapMode

strong

Texture coordinate wrapping mode.

Enumerator
Extend	Image edges are extended outside the image, i.e. sample coordinates are clamped to the edge.
Repeat	Image repeats, i.e. sample coordinates are wrapped around.
Border	Samples outside the image return transparent black.

Definition at line 34 of file BLI_math_interp.hh.

Function Documentation

◆ abs() [1/3]

template<>

AxisSigned blender::math::abs ( const AxisSigned & axis )

inline

Definition at line 201 of file BLI_math_basis_types.hh.

References blender::math::AxisSigned::axis().

◆ abs() [2/3]

template<typename T>

T blender::math::abs ( const T & a )

inline

Definition at line 33 of file BLI_math_base.hh.

References T.

◆ abs() [3/3]

template<typename T, int Size>

VecBase< T, Size > blender::math::abs ( const VecBase< T, Size > & a )

inlinenodiscard

Definition at line 38 of file BLI_math_vector.hh.

References i, and result.

◆ acos()

template<typename T>

T blender::math::acos ( const T & a )

inline

Definition at line 189 of file BLI_math_base.hh.

References T.

Referenced by blender::noise::compute_3d_orientation(), interpolate_dot_slerp(), and safe_acos().

◆ adjoint() [1/7]

template double2x2 blender::math::adjoint ( const double2x2 & mat )

◆ adjoint() [2/7]

template double3x3 blender::math::adjoint ( const double3x3 & mat )

◆ adjoint() [3/7]

template double4x4 blender::math::adjoint ( const double4x4 & mat )

◆ adjoint() [4/7]

template float2x2 blender::math::adjoint ( const float2x2 & mat )

◆ adjoint() [5/7]

template float3x3 blender::math::adjoint ( const float3x3 & mat )

◆ adjoint() [6/7]

template float4x4 blender::math::adjoint ( const float4x4 & mat )

◆ adjoint() [7/7]

template<typename T, int Size>

MatBase< T, Size, Size > blender::math::adjoint ( const MatBase< T, Size, Size > & mat )

nodiscard

Returns the adjoint of the matrix (also known as adjugate matrix).

Definition at line 165 of file math_matrix.cc.

References determinant(), T, and blender::unroll().

◆ almost_equal_relative()

template<typename T, int Size>

bool blender::math::almost_equal_relative	(	const VecBase< T, Size > &	a,
		const VecBase< T, Size > &	b,
		const T &	epsilon_factor )

inlinenodiscard

Returns true if the given vectors are equal within the given epsilon. The epsilon is scaled for each component by magnitude of the matching component of a.

Definition at line 25 of file BLI_math_vector.hh.

References abs(), b, distance(), i, and T.

Referenced by blender::bke::CurvesGeometry::evaluated_tangents().

◆ angle_between() [1/3]

template<typename T>

AngleFraction< T > blender::math::angle_between	(	const AxisSigned	a,
		const AxisSigned	b )

nodiscard

Definition at line 163 of file BLI_math_rotation.hh.

References abs, b, blender::math::AngleFraction< T >::identity(), and blender::math::AngleFraction< T >::pi().

◆ angle_between() [2/3]

template<typename T>

AngleRadianBase< T > blender::math::angle_between	(	const QuaternionBase< T > &	a,
		const QuaternionBase< T > &	b )

nodiscard

Extract angle between 2 orientations. For Quaternion, the returned angle is in [0..2pi] range. For other types, the returned angle is in [0..pi] range. See angle_of for more detail.

Definition at line 150 of file BLI_math_rotation.hh.

References angle_of(), b, and rotation_between().

Referenced by blender::ed::sculpt_paint::greasepencil::compute_auto_flip(), blender::geometry::extend_curve_curved(), blender::math::tests::TEST(), and blender::bke::pbvh::uv_islands::UVBorderCorner::uv().

◆ angle_between() [3/3]

template<typename T>

AngleRadianBase< T > blender::math::angle_between	(	const VecBase< T, 3 > &	a,
		const VecBase< T, 3 > &	b )

nodiscard

Definition at line 156 of file BLI_math_rotation.hh.

References b, BLI_assert, dot(), is_unit_scale(), and safe_acos().

◆ angle_between_signed()

template<typename T>

AngleRadianBase< T > blender::math::angle_between_signed	(	const QuaternionBase< T > &	a,
		const QuaternionBase< T > &	b )

nodiscard

Extract angle between 2 orientations. Returned angle is in [-pi..pi] range. See angle_of_signed for more detail.

Definition at line 180 of file BLI_math_rotation.hh.

References angle_of_signed(), b, and rotation_between().

Referenced by blender::math::tests::TEST().

◆ angle_of()

template<typename T>

AngleRadianBase< T > blender::math::angle_of ( const QuaternionBase< T > & q )

nodiscard

Extract rotation angle from a unit quaternion. Returned angle is in [0..2pi] range.

Unlike the angle between vectors, this does NOT return the shortest angle. See angle_of_signed below for this.

Definition at line 123 of file BLI_math_rotation.hh.

References BLI_assert, is_unit_scale(), safe_acos(), T, and blender::math::QuaternionBase< T >::w.

Referenced by angle_between(), blender::nodes::node_fn_combine_transform_cc::CombineTransformFunction::call(), blender::math::tests::TEST(), and blender::nodes::node_geo_transform_geometry_cc::use_translate().

◆ angle_of_signed()

template<typename T>

AngleRadianBase< T > blender::math::angle_of_signed ( const QuaternionBase< T > & q )

nodiscard

Extract rotation angle from a unit quaternion. Always return the shortest angle. Returned angle is in [-pi..pi] range.

angle_of with quaternion can exceed PI radians. Having signed versions of these functions allows to use 'abs(angle_of_signed(...))' to get the shortest angle between quaternions with higher precision than subtracting 2pi afterwards.

Definition at line 137 of file BLI_math_rotation.hh.

References BLI_assert, is_unit_scale(), safe_acos(), T, and blender::math::QuaternionBase< T >::w.

Referenced by angle_between_signed(), and blender::math::tests::TEST().

◆ asin()

template<typename T>

T blender::math::asin ( const T & a )

inline

Definition at line 253 of file BLI_math_base.hh.

References T.

◆ atan()

template<typename T>

T blender::math::atan ( const T & a )

inline

Definition at line 258 of file BLI_math_base.hh.

References T.

Referenced by blender::tests::TEST().

◆ atan2()

template<typename T>

T blender::math::atan2	(	const T &	y,
		const T &	x )

inline

Definition at line 263 of file BLI_math_base.hh.

References T, x, and y.

Referenced by blender::math::AngleRadianBase< float >::AngleRadianBase(), blender::compositor::bokeh(), blender::nodes::node_composite_chroma_matte_cc::chroma_matte(), from_triangle(), blender::noise::gabor(), blender::noise::gabor(), blender::ed::greasepencil::generate_arc_from_point_to_point(), blender::ed::greasepencil::grease_pencil_primitive_rotate_all_update(), blender::math::detail::normalized_to_eul2(), blender::math::detail::normalized_to_eul2(), blender::math::AngleCartesianBase< float >::operator float(), blender::bke::greasepencil::Drawing::set_texture_matrices(), to_quaternion_legacy(), and blender::write_fill_transforms().

◆ average()

template<typename T, int Size>

T blender::math::average ( const VecBase< T, Size > & a )

inlinenodiscard

Returns: the average of the components of a vector.

Definition at line 723 of file BLI_math_vector.hh.

References reduce_add(), and T.

Referenced by blender::ed::greasepencil::create_curves_outline(), blender::ed::greasepencil::image_render::create_shader_ubo(), blender::ed::greasepencil::image_render::draw_circles(), blender::ed::sculpt_paint::grease_pencil_fill_extension_lines_from_circles(), blender::io::grease_pencil::shape_attributes_to_curves(), and blender::ed::view3d::geometry_nodes_gizmos::DialGizmo::update_transform().

◆ bicubic_interpolation()

template<typename T, eCubicFilter filter>

BLI_INLINE void blender::math::bicubic_interpolation	(	const T *	src_buffer,
		T *	output,
		int	width,
		int	height,
		int	components,
		float	u,
		float	v,
		InterpWrapMode	wrap_u,
		InterpWrapMode	wrap_v )

Definition at line 152 of file math_interp.cc.

References BLI_assert, BLI_INLINE, Border, copy_v2_v2(), copy_v3_v3(), copy_v4_v4(), cubic_filter_coefficients(), data, Extend, filter, float, floor, i, max(), min(), Mitchell, out, output, T, v, w(), and wrap_coord().

Referenced by interpolate_cubic_bspline_byte(), interpolate_cubic_bspline_fl(), interpolate_cubic_bspline_fl(), interpolate_cubic_bspline_wrapmode_fl(), interpolate_cubic_mitchell_byte(), interpolate_cubic_mitchell_fl(), and interpolate_cubic_mitchell_fl().

◆ bilinear_byte_impl()

template<bool border>

BLI_INLINE uchar4 blender::math::bilinear_byte_impl	(	const uchar *	buffer,
		int	width,
		int	height,
		float	u,
		float	v )

Definition at line 418 of file math_interp.cc.

References b, BLI_assert, BLI_INLINE, clamp(), floorf, and v.

Referenced by interpolate_bilinear_border_byte(), and interpolate_bilinear_byte().

◆ bilinear_fl_impl()

BLI_INLINE void blender::math::bilinear_fl_impl	(	const float *	buffer,
		float *	output,
		int	width,
		int	height,
		int	components,
		float	u,
		float	v,
		InterpWrapMode	wrap_x,
		InterpWrapMode	wrap_y )

Definition at line 287 of file math_interp.cc.

References b, BLI_assert, BLI_INLINE, Border, clamp(), copy_vn_fl(), floored_fmod(), floorf, output, Repeat, and v.

Referenced by interpolate_bilinear_border_fl(), interpolate_bilinear_border_fl(), interpolate_bilinear_fl(), interpolate_bilinear_fl(), interpolate_bilinear_wrap_fl(), and interpolate_bilinear_wrapmode_fl().

◆ canonicalize()

template<typename T>

QuaternionBase< T > blender::math::canonicalize ( const QuaternionBase< T > & q )

inlinenodiscard

Negate the quaternion if real component (w) is negative.

Definition at line 227 of file BLI_math_quaternion.hh.

References T, and blender::math::QuaternionBase< T >::w.

Referenced by blender::math::QuaternionBase< T >::swing(), blender::math::tests::TEST(), blender::math::QuaternionBase< T >::twist(), and blender::math::QuaternionBase< T >::twist_angle().

◆ ceil() [1/2]

template<typename T>

T blender::math::ceil ( const T & a )

inline

Definition at line 138 of file BLI_math_base.hh.

References T.

◆ ceil() [2/2]

template<typename T, int Size>

VecBase< T, Size > blender::math::ceil ( const VecBase< T, Size > & a )

inlinenodiscard

Definition at line 364 of file BLI_math_vector.hh.

References BLI_UNROLL_MATH_VEC_OP_VEC, and ceil().

◆ ceil_to_multiple()

template<typename T, int Size>

VecBase< T, Size > blender::math::ceil_to_multiple	(	const VecBase< T, Size > &	a,
		const VecBase< T, Size > &	b )

inlinenodiscard

Returns a if it is a multiple of b or the next multiple or b after a . In other words, it is equivalent to divide_ceil(a, b) * b. It is undefined if a is negative or b is not strictly positive.

Definition at line 296 of file BLI_math_vector.hh.

References b, BLI_assert, i, and result.

Referenced by blender::eevee::DepthOfField::sync(), blender::eevee::HiZBuffer::sync(), and blender::tests::TEST().

◆ chromatic_adaption_matrix()

float3x3 blender::math::chromatic_adaption_matrix	(	const float3 &	from_XYZ,
		const float3 &	to_XYZ )

Definition at line 884 of file math_color.cc.

References from_scale(), and invert().

Referenced by blender::ocio::calculate_white_point_matrix(), blender::nodes::node_composite_colorbalance_cc::get_white_point_matrix(), and blender::nodes::node_composite_colorbalance_cc::white_point_variable().

◆ clamp() [1/3]

template<typename T>

T blender::math::clamp	(	const T &	a,
		const T &	min,
		const T &	max )

inline

Definition at line 69 of file BLI_math_base.hh.

References max(), min(), and T.

◆ clamp() [2/3]

template<typename T, int Size>

VecBase< T, Size > blender::math::clamp	(	const VecBase< T, Size > &	a,
		const T &	min,
		const T &	max )

inlinenodiscard

Definition at line 131 of file BLI_math_vector.hh.

References clamp(), i, max(), min(), result, and T.

◆ clamp() [3/3]

template<typename T, int Size>

VecBase< T, Size > blender::math::clamp	(	const VecBase< T, Size > &	a,
		const VecBase< T, Size > &	min,
		const VecBase< T, Size > &	max )

inlinenodiscard

Definition at line 119 of file BLI_math_vector.hh.

References clamp(), i, max(), min(), and result.

◆ conjugate()

template<typename T>

QuaternionBase< T > blender::math::conjugate ( const QuaternionBase< T > & a )

inlinenodiscard

Return the conjugate of the given quaternion. If the quaternion q represent the rotation from A to B, then the conjugate of q represents the rotation from B to A.

Definition at line 221 of file BLI_math_quaternion.hh.

References blender::math::QuaternionBase< T >::w, blender::math::QuaternionBase< T >::x, blender::math::QuaternionBase< T >::y, and blender::math::QuaternionBase< T >::z.

Referenced by from_triangle(), invert(), invert_normalized(), blender::math::tests::TEST(), to_quaternion_legacy(), and transform_point().

◆ cos() [1/4]

template<typename T>

T blender::math::cos ( const AngleCartesianBase< T > & a )

Definition at line 697 of file BLI_math_angle_types.hh.

References blender::math::AngleCartesianBase< T >::cos(), and T.

◆ cos() [2/4]

template<typename T>

T blender::math::cos ( const AngleFraction< T > & a )

Definition at line 710 of file BLI_math_angle_types.hh.

References cos, and T.

◆ cos() [3/4]

template<typename T>

T blender::math::cos ( const AngleRadianBase< T > & a )

Definition at line 684 of file BLI_math_angle_types.hh.

References cos, blender::math::AngleRadianBase< T >::radian(), and T.

Referenced by blender::math::AngleRadianBase< float >::AngleRadianBase(), blender::math::AxisAngleBase< T, AngleT >::AxisAngleBase(), blender::noise::compute_2d_gabor_kernel(), blender::noise::compute_3d_gabor_kernel(), blender::noise::compute_3d_orientation(), blender::compositor::compute_denominator_1(), blender::compositor::compute_denominator_2(), blender::compositor::compute_denominator_3(), blender::compositor::compute_numerator_1(), blender::compositor::compute_numerator_2(), blender::compositor::compute_numerator_3(), blender::nodes::node_composite_glare_cc::GlareOperation::compute_streak_direction(), blender::bke::tests::GreasePencilInterpolate::create_test_shape(), blender::nodes::node_composite_kuwahara_cc::ConvertKuwaharaOperation::execute_anisotropic_cpu(), blender::nodes::node_composite_boxmask_cc::BoxMaskOperation::execute_cpu(), blender::nodes::node_composite_directionalblur_cc::DirectionalBlurOperation::execute_cpu(), blender::nodes::node_composite_ellipsemask_cc::EllipseMaskOperation::execute_cpu(), blender::nodes::node_composite_split_cc::SplitOperation::execute_cpu(), blender::nodes::node_composite_directionalblur_cc::DirectionalBlurOperation::execute_gpu(), blender::nodes::node_composite_split_cc::SplitOperation::execute_gpu(), blender::workbench::filter_blackman_harris(), blender::math::detail::from_rotation(), from_triangle(), blender::ed::greasepencil::generate_arc_from_point_to_point(), blender::ed::greasepencil::generate_circle_from_point(), blender::ed::greasepencil::generate_corner(), blender::compositor::get_regular_polygon_vertex_position(), blender::ed::greasepencil::grease_pencil_primitive_rotate_all_update(), blender::workbench::SceneResources::load_jitter_tx(), blender::math::AngleFraction< T >::operator AngleCartesianBase< T >(), pow(), blender::ed::sculpt_paint::greasepencil::PaintOperationExecutor::process_extension_sample(), blender::draw::overlay::ring_vertices(), blender::ed::sculpt_paint::greasepencil::rotate_by_angle(), blender::rotate_by_angle(), blender::draw::statvis_calc_thickness(), blender::tests::TEST(), to_quaternion(), to_quaternion(), to_quaternion_legacy(), and blender::write_fill_transforms().

◆ cos() [4/4]

template<typename T>

T blender::math::cos ( const T & a )

inline

Definition at line 174 of file BLI_math_base.hh.

References T.

◆ cross() [1/3]

AxisSigned blender::math::cross	(	const AxisSigned	a,
		const AxisSigned	b )

inlinenodiscard

Returns the cross direction from two basis direction using the right hand rule. This is much faster than true cross product if the vectors are basis vectors. Any ill-formed case will return a orthogonal axis to a but will also trigger an assert. It is better to filter these cases upstream.

Definition at line 217 of file BLI_math_basis_types.hh.

References abs, b, BLI_assert_msg, blender::math::AxisSigned::next_after(), blender::math::AxisSigned::X_NEG, blender::math::AxisSigned::X_POS, blender::math::AxisSigned::Y_NEG, blender::math::AxisSigned::Y_POS, blender::math::AxisSigned::Z_NEG, and blender::math::AxisSigned::Z_POS.

◆ cross() [2/3]

template<typename T>

T blender::math::cross	(	const VecBase< T, 2 > &	a,
		const VecBase< T, 2 > &	b )

inlinenodiscard

Definition at line 543 of file BLI_math_vector.hh.

References b, and T.

◆ cross() [3/3]

template<typename T>

VecBase< T, 3 > blender::math::cross	(	const VecBase< T, 3 > &	a,
		const VecBase< T, 3 > &	b )

inlinenodiscard

Returns: cross perpendicular vector to a and b.

Note: Return zero vector if a and b are collinear.; The length of the resulting vector is equal to twice the area of the triangle between a and b ; and it is equal to the sine of the angle between a and b if they are normalized.; Blender 3D space uses right handedness: a = thumb, b = index, return = middle.

Definition at line 557 of file BLI_math_vector.hh.

References b.

◆ cross_high_precision()

VecBase< float, 3 > blender::math::cross_high_precision	(	const VecBase< float, 3 > &	a,
		const VecBase< float, 3 > &	b )

inlinenodiscard

Same as cross(a, b) but use double float precision for the computation.

Definition at line 565 of file BLI_math_vector.hh.

References b, and float.

Referenced by blender::nodes::node_fn_align_euler_to_vector_cc::align_rotations_auto_pivot(), blender::nodes::node_fn_align_rotation_to_vector_cc::align_rotations_auto_pivot(), damptrack_do_transform(), and blender::nodes::try_dispatch_float_math_fl3_fl3_to_fl3().

◆ cross_poly()

template<typename T>

VecBase< T, 3 > blender::math::cross_poly ( Span< VecBase< T, 3 > > poly )

inlinenodiscard

Parameters

poly	Array of points around a polygon. They don't have to be co-planar.

Returns: Best fit plane normal for the given polygon loop or zero vector if point array is too short. Not normalized.

Definition at line 578 of file BLI_math_vector.hh.

References i.

Referenced by get_dupliface_transform_from_coords().

◆ cross_tri()

template<typename T>

VecBase< T, 3 > blender::math::cross_tri	(	const VecBase< T, 3 > &	v1,
		const VecBase< T, 3 > &	v2,
		const VecBase< T, 3 > &	v3 )

inlinenodiscard

Return normal vector to a triangle. The result is not normalized and can be degenerate.

Definition at line 606 of file BLI_math_vector.hh.

References cross, and v2.

Referenced by normal_tri().

◆ cube()

template<typename T>

T blender::math::cube ( const T & a )

inline

Definition at line 214 of file BLI_math_base.hh.

References T.

Referenced by blender::compositor::compute_fog_glow_kernel_value(), and blender::eevee::LightProbeModule::end_sync().

◆ cubic_filter_coefficients()

template<enum eCubicFilter filter>

float4 blender::math::cubic_filter_coefficients ( float f )

static

Definition at line 76 of file math_interp.cc.

References BSpline, filter, and Mitchell.

Referenced by bicubic_interpolation().

◆ determinant() [1/7]

template double blender::math::determinant ( const double2x2 & mat )

◆ determinant() [2/7]

template double blender::math::determinant ( const double3x3 & mat )

◆ determinant() [3/7]

template double blender::math::determinant ( const double4x4 & mat )

◆ determinant() [4/7]

template float blender::math::determinant ( const float2x2 & mat )

◆ determinant() [5/7]

template float blender::math::determinant ( const float3x3 & mat )

◆ determinant() [6/7]

template float blender::math::determinant ( const float4x4 & mat )

◆ determinant() [7/7]

template<typename T, int Size>

T blender::math::determinant ( const MatBase< T, Size, Size > & mat )

nodiscard

Returns the determinant of the matrix. It can be interpreted as the signed volume (or area) of the unit cube after transformation.

Definition at line 131 of file math_matrix.cc.

References blender::MatBase< T, NumCol, NumRow, Alignment >::base_ptr(), and T.

Referenced by BKE_volume_grid_transform_valid(), blender::nodes::node_fn_axes_to_rotation_cc::AxesToRotationFunction::call(), blender::bke::tests::EXPECT_M3_ORTHOGONAL(), IMB_colormanagement_working_space_convert(), blender::nodes::node_fn_matrix_determinant_cc::node_build_multi_function(), blender::math::detail::normalized_to_quat_with_checks(), blender::bke::greasepencil::Drawing::set_texture_matrices(), blender::geometry::transform_volume(), and blender::ed::view3d::geometry_nodes_gizmos::DialGizmo::update_transform().

◆ distance() [1/2]

template<typename T>

T blender::math::distance	(	const T &	a,
		const T &	b )

inline

Definition at line 143 of file BLI_math_base.hh.

References b, and T.

◆ distance() [2/2]

template<typename T, int Size>

T blender::math::distance	(	const VecBase< T, Size > &	a,
		const VecBase< T, Size > &	b )

inlinenodiscard

Definition at line 480 of file BLI_math_vector.hh.

References b, length(), and T.

◆ distance_manhattan()

template<typename T, int Size>

T blender::math::distance_manhattan	(	const VecBase< T, Size > &	a,
		const VecBase< T, Size > &	b )

inlinenodiscard

Definition at line 468 of file BLI_math_vector.hh.

References b, length_manhattan(), and T.

◆ distance_squared()

template<typename T, int Size>

T blender::math::distance_squared	(	const VecBase< T, Size > &	a,
		const VecBase< T, Size > &	b )

inlinenodiscard

Definition at line 474 of file BLI_math_vector.hh.

References b, length_squared(), and T.

◆ divide_ceil()

template<typename T, int Size>

VecBase< T, Size > blender::math::divide_ceil	(	const VecBase< T, Size > &	a,
		const VecBase< T, Size > &	b )

inlinenodiscard

Integer division that returns the ceiling, instead of flooring like normal C division. It is undefined if a is negative or b is not strictly positive.

Definition at line 313 of file BLI_math_vector.hh.

References b, BLI_assert, i, and result.

◆ dominant_axis()

template<typename T>

int blender::math::dominant_axis ( const VecBase< T, 3 > & a )

inlinenodiscard

Returns: Index of the component with the greatest magnitude.

Definition at line 662 of file BLI_math_vector.hh.

References abs, and b.

Referenced by blender::draw::overlay::Fluids::begin_sync(), blender::bke::pbvh::build_nodes_recursive_grids(), blender::bke::pbvh::build_nodes_recursive_mesh(), orthogonal(), blender::bke::partition_faces_recursively(), blender::bke::pbvh::pbvh_bmesh_node_limit_ensure_fast(), and blender::bke::pbvh::pbvh_bmesh_node_split().

◆ dot() [1/2]

template<typename T>

T blender::math::dot	(	const QuaternionBase< T > &	a,
		const QuaternionBase< T > &	b )

inlinenodiscard

Dot product between two quaternions. Equivalent to vector dot product. Equivalent to component wise multiplication followed by summation of the result.

Definition at line 197 of file BLI_math_quaternion.hh.

References b, T, blender::math::QuaternionBase< T >::w, blender::math::QuaternionBase< T >::x, blender::math::QuaternionBase< T >::y, and blender::math::QuaternionBase< T >::z.

◆ dot() [2/2]

template<typename T, int Size>

T blender::math::dot	(	const VecBase< T, Size > &	a,
		const VecBase< T, Size > &	b )

inlinenodiscard

Dot product between two vectors. Equivalent to component wise multiplication followed by summation of the result. Equivalent to the cosine of the angle between the two vectors if the vectors are normalized.

Note: prefer using length_manhattan(a) than dot(a, vec(1)) to get the sum of all components.

Definition at line 425 of file BLI_math_vector.hh.

References b, i, result, and T.

◆ exp() [1/2]

template<typename T>

T blender::math::exp ( const T & x )

inline

◆ exp() [2/2]

template<typename T, int Size>

VecBase< T, Size > blender::math::exp ( const VecBase< T, Size > & x )

inlinenodiscard

Definition at line 285 of file BLI_math_vector.hh.

References BLI_UNROLL_MATH_VEC_OP_VEC, exp(), and x.

◆ faceforward()

template<typename T, int Size>

VecBase< T, Size > blender::math::faceforward	(	const VecBase< T, Size > &	vector,
		const VecBase< T, Size > &	incident,
		const VecBase< T, Size > &	reference )

inlinenodiscard

Return vector if incident and reference are pointing in the same direction.

Definition at line 652 of file BLI_math_vector.hh.

References dot().

◆ fallback_pow() [1/2]

template<typename T>

T blender::math::fallback_pow	(	const T &	x,
		const T &	power,
		const T &	fallback )

inline

Definition at line 204 of file BLI_math_base.hh.

References power(), T, and x.

Referenced by blender::nodes::node_composite_colorcorrection_cc::color_correction(), and fallback_pow().

◆ fallback_pow() [2/2]

template<typename T, int Size>

VecBase< T, Size > blender::math::fallback_pow	(	const VecBase< T, Size > &	x,
		const T &	y,
		const VecBase< T, Size > &	fallback )

inlinenodiscard

Return the value of x raised to the y power. The result is the given fallback if x < 0 or if x = 0 and y <= 0.

Definition at line 256 of file BLI_math_vector.hh.

References fallback_pow(), i, result, T, x, and y.

◆ float_to_half()

uint16_t blender::math::float_to_half ( float v )

Float (FP32) <-> Half (FP16) conversion functions.

Behavior matches hardware (x64 F16C, ARM NEON FCVT), including handling of denormals, infinities, NaNs, rounding is to nearest even, etc. When NaNs are produced, the exact bit pattern might not match hardware, but it will still be a NaN.

When compiling for ARM NEON (e.g. Apple Silicon), hardware VCVT instructions are used.

For anything involving more than a handful of numbers, prefer float_to_half_array and half_to_float_array for performance. Converts float (FP32) number to half-precision (FP16).

Definition at line 27 of file math_half.cc.

References sign(), and v.

Referenced by blender::gpu::convert(), blender::gpu::convert(), float_to_half_array(), and float_to_half_make_finite().

◆ float_to_half_array()

void blender::math::float_to_half_array	(	const float *	src,
		uint16_t *	dst,
		size_t	length )

Definition at line 238 of file math_half.cc.

References float_to_half(), i, and length().

Referenced by blender::tests::TEST().

◆ float_to_half_make_finite()

uint16_t blender::math::float_to_half_make_finite ( float v )

Converts float (FP32) number to half-precision (FP16), also ensuring the result is finite.

Changes +/- infinities to +/- maximum value (65504), and NaNs to zeroes.

Definition at line 91 of file math_half.cc.

References float_to_half(), and v.

Referenced by float_to_half_make_finite_array().

◆ float_to_half_make_finite_array()

void blender::math::float_to_half_make_finite_array	(	const float *	src,
		uint16_t *	dst,
		size_t	length )

Definition at line 274 of file math_half.cc.

References float_to_half_make_finite(), i, and length().

Referenced by blender::gpu::convert_buffer(), blender::tests::TEST(), blender::gpu::GLTexture::update_sub(), and blender::gpu::MTLTexture::update_sub().

◆ floor() [1/2]

template<typename T>

T blender::math::floor ( const T & a )

inline

Definition at line 112 of file BLI_math_base.hh.

References T.

◆ floor() [2/2]

template<typename T, int Size>

VecBase< T, Size > blender::math::floor ( const VecBase< T, Size > & a )

inlinenodiscard

Definition at line 352 of file BLI_math_vector.hh.

References BLI_UNROLL_MATH_VEC_OP_VEC, and floor().

◆ floored_mod() [1/3]

template<typename T>

T blender::math::floored_mod	(	const T &	a,
		const T &	b )

inline

Definition at line 89 of file BLI_math_base.hh.

References b, and T.

Referenced by floored_mod(), and floored_mod().

◆ floored_mod() [2/3]

template<typename T, int Size>

VecBase< T, Size > blender::math::floored_mod	(	const VecBase< T, Size > &	a,
		const T &	b )

inlinenodiscard

Definition at line 213 of file BLI_math_vector.hh.

References b, BLI_assert, floored_mod(), i, result, and T.

◆ floored_mod() [3/3]

template<typename T, int Size>

VecBase< T, Size > blender::math::floored_mod	(	const VecBase< T, Size > &	a,
		const VecBase< T, Size > &	b )

inlinenodiscard

Definition at line 201 of file BLI_math_vector.hh.

References b, BLI_assert, floored_mod(), i, and result.

◆ fract() [1/2]

template<typename T>

T blender::math::fract ( const T & a )

inline

Definition at line 148 of file BLI_math_base.hh.

References T.

Referenced by blender::deform_drawing(), blender::deform_drawing(), blender::eevee::VolumeModule::draw_prepass(), fract(), blender::nodes::node_composite_huecorrect_cc::hue_correct(), blender::nodes::node_composite_vec_blur_cc::interleaved_gradient_noise(), blender::nodes::node_composite_hue_sat_val_cc::node_build_multi_function(), and blender::table_sample().

◆ fract() [2/2]

template<typename T, int Size>

VecBase< T, Size > blender::math::fract ( const VecBase< T, Size > & a )

inlinenodiscard

Definition at line 413 of file BLI_math_vector.hh.

References BLI_UNROLL_MATH_VEC_OP_VEC, and fract().

◆ from_direction()

template<typename T>

MatBase< T, 2, 2 > blender::math::from_direction ( const VecBase< T, 2 > & direction )

nodiscard

Create a rotation matrix with the angle that the given direction makes with the x axis. Assumes the direction vector is normalized.

Definition at line 1477 of file BLI_math_matrix.hh.

References BLI_assert, and is_unit_scale().

Referenced by blender::nodes::node_composite_chroma_matte_cc::chroma_matte().

◆ from_loc_rot()

template<typename MatT, typename RotationT>

MatT blender::math::from_loc_rot	(	const typename MatT::loc_type &	location,
		const RotationT &	rotation )

nodiscard

Create a transform matrix with translation and rotation applied in this order.

Definition at line 1459 of file BLI_math_matrix.hh.

References from_rotation().

Referenced by blender::math::tests::TEST(), blender::tests::TEST(), and blender::tests::TEST().

◆ from_loc_rot_scale()

template<typename MatT, typename RotationT, int ScaleDim>

MatT blender::math::from_loc_rot_scale	(	const typename MatT::loc_type &	location,
		const RotationT &	rotation,
		const VecBase< typename MatT::base_type, ScaleDim > &	scale )

nodiscard

Create a transform matrix with translation, rotation and scale applied in this order.

Definition at line 1447 of file BLI_math_matrix.hh.

References from_rot_scale(), and scale().

Referenced by blender::nodes::node_geo_instance_on_points_cc::add_instances_from_component(), blender::ed::curves::append_primitive_curve(), blender::apply_stroke_transform(), blender::draw::overlay::Cursor::begin_sync(), blender::seq::calc_strip_transform_matrix(), blender::nodes::node_fn_combine_transform_cc::CombineTransformFunction::call(), blender::nodes::node_composite_stabilize2d_cc::Stabilize2DOperation::execute(), blender::nodes::node_composite_transform_cc::TransformOperation::execute(), blender::bke::attribute_math::float4x4Mixer::finalize(), blender::get_rand_matrix(), interpolate_fast(), blender::bke::greasepencil::Layer::local_transform(), blender::bke::attribute_math::mix3(), blender::bke::attribute_math::mix4(), blender::nodes::node_fn_separate_transform_cc::node_eval_inverse(), blender::nodes::node_geo_transform_geometry_cc::node_geo_exec(), blender::draw::overlay::LightProbes::object_sync(), blender::seq::seq_image_transform_matrix_get_ex(), blender::eevee::IrradianceBake::surfel_raster_views_sync(), blender::imbuf::tests::TEST(), blender::math::tests::TEST(), blender::tests::TEST(), blender::tests::TEST(), blender::tests::TEST(), blender::draw::test_eevee_shadow_tag_update(), and blender::geometry::transform_mesh().

◆ from_loc_scale()

template<typename MatT, int ScaleDim>

MatT blender::math::from_loc_scale	(	const typename MatT::loc_type &	location,
		const VecBase< typename MatT::base_type, ScaleDim > &	scale )

nodiscard

Create a transform matrix with translation and scale applied in this order.

Definition at line 1469 of file BLI_math_matrix.hh.

References from_scale(), and scale().

Referenced by blender::ed::greasepencil::fit_strokes_to_view(), blender::draw::overlay::Fluids::object_sync(), and blender::draw::overlay::GreasePencil::object_sync().

◆ from_location()

template<typename MatT>

MatT blender::math::from_location ( const typename MatT::loc_type & location )

nodiscard

Create a translation only matrix. Matrix dimensions should be at least 4 col x 3 row.

Definition at line 1416 of file BLI_math_matrix.hh.

Referenced by blender::nodes::node_fn_combine_transform_cc::CombineTransformFunction::call(), blender::compositor::RealizeOnDomainOperation::compute_realized_transformation_domain(), blender::nodes::node_composite_displace_cc::DisplaceOperation::execute(), blender::nodes::node_composite_translate_cc::TranslateOperation::execute(), from_origin_transform(), blender::get_array_matrix(), blender::seq::input_preprocess(), blender::nodes::node_geo_scale_instances_cc::scale_instances(), blender::eevee::VolumeProbeModule::set_view(), blender::tests::TEST(), blender::nodes::node_geo_translate_instances_cc::translate_instances(), and blender::geometry::translate_volume().

◆ from_origin_transform()

template<typename MatT, typename VectorT>

MatT blender::math::from_origin_transform	(	const MatT &	transform,
		const VectorT	origin )

nodiscard

Construct a transformation that is pivoted around the given origin point. So for instance, from_origin_transform<MatT>(from_rotation(numbers::pi * 0.5), float2(0.0f, 2.0f)) will construct a transformation representing a 90 degree rotation around the point (0, 2).

Definition at line 1623 of file BLI_math_matrix.hh.

References from_location(), and transform().

Referenced by blender::seq::calc_strip_transform_matrix(), blender::compositor::RealizeOnDomainOperation::compute_realized_transformation_domain(), and blender::seq::seq_image_transform_matrix_get_ex().

◆ from_orthonormal_axes() [1/3]

CartesianBasis blender::math::from_orthonormal_axes	(	const AxisSigned	forward,
		const AxisSigned	up )

inlinenodiscard

Create an CartesianBasis using two orthogonal axes. The third axis is chosen by right hand rule to follow blender coordinate system. forward is Y axis in blender coordinate system. up is Z axis in blender coordinate system.

Note: forward and up must be different axes.

Definition at line 405 of file BLI_math_basis_types.hh.

References abs(), BLI_assert, and cross.

Referenced by from_orthonormal_axes(), from_tracking(), blender::eevee::IrradianceBake::raylists_build(), rotation_between(), blender::math::tests::TEST(), blender::math::tests::TEST(), and blender::math::tests::TEST().

◆ from_orthonormal_axes() [2/3]

template<typename MatT, typename VectorT>

MatT blender::math::from_orthonormal_axes	(	const VectorT	forward,
		const VectorT	up )

nodiscard

Create a rotation matrix from 2 basis vectors. The matrix determinant is given to be positive and it can be converted to other rotation types.

Note: forward and up must be normalized.

Definition at line 1485 of file BLI_math_matrix.hh.

References BLI_assert, cross(), and is_unit_scale().

◆ from_orthonormal_axes() [3/3]

template<typename MatT, typename VectorT>

MatT blender::math::from_orthonormal_axes	(	const VectorT	location,
		const VectorT	forward,
		const VectorT	up )

nodiscard

Create a transform matrix with translation and rotation from 2 basis vectors and a translation.

Note: forward and up must be normalized.

Definition at line 1501 of file BLI_math_matrix.hh.

References from_orthonormal_axes().

◆ from_rot_scale()

template<typename MatT, typename RotationT, typename VectorT>

MatT blender::math::from_rot_scale	(	const RotationT &	rotation,
		const VectorT &	scale )

nodiscard

Create a transform matrix with rotation and scale applied in this order.

Definition at line 1441 of file BLI_math_matrix.hh.

References from_rotation(), from_scale(), and scale().

Referenced by from_loc_rot_scale(), interpolate_fast(), and blender::tests::TEST().

◆ from_rotation()

template<typename MatT, typename RotationT>

MatT blender::math::from_rotation ( const RotationT & rotation )

nodiscard

Create a rotation only matrix.

Definition at line 1435 of file BLI_math_matrix.hh.

References blender::math::detail::from_rotation().

Referenced by blender::draw::overlay::Cursor::begin_sync(), blender::nodes::node_fn_combine_transform_cc::CombineTransformFunction::call(), blender::nodes::node_composite_rotate_cc::RotateOperation::execute(), blender::geometry::extend_curve_curved(), from_loc_rot(), from_rot_scale(), blender::nodes::node_composite_directionalblur_cc::DirectionalBlurOperation::get_delta_translation(), blender::ed::greasepencil::grease_pencil_texture_gradient_exec(), interpolate(), blender::ed::view3d::geometry_nodes_gizmos::matrix_from_position_and_up_direction(), blender::ed::sculpt_paint::paint_cursor_drawing_setup_cursor_space(), blender::bke::quaternion_to_float4x4(), blender::io::grease_pencil::SVGImporter::read(), rotate(), rotate(), rotate(), blender::nodes::node_geo_rotate_instances_cc::rotate_instances(), blender::eevee::IrradianceBake::surfel_raster_views_sync(), blender::math::tests::TEST(), blender::tests::TEST(), blender::tests::TEST(), blender::tests::TEST(), blender::tests::TEST(), blender::tests::TEST(), TEST(), to_dual_quaternion(), to_euler(), to_euler(), to_gimbal_axis(), blender::ed::view3d::geometry_nodes_gizmos::TransformGizmos::update(), blender::ed::view3d::geometry_nodes_gizmos::TransformGizmos::update_rotate_transform_and_target_property(), blender::ed::view3d::geometry_nodes_gizmos::TransformGizmos::update_scale_transform_and_target_property(), and blender::bke::pbvh::uv_islands::UVBorderCorner::uv().

◆ from_scale()

template<typename MatT, int ScaleDim>

MatT blender::math::from_scale ( const VecBase< typename MatT::base_type, ScaleDim > & scale )

nodiscard

Create a matrix whose diagonal is defined by the given scale vector. If vector dimension is lower than matrix diagonal, the missing terms are filled with ones.

Definition at line 1424 of file BLI_math_matrix.hh.

References BLI_STATIC_ASSERT, i, result, scale(), and blender::unroll().

Referenced by blender::draw::overlay::Cursor::begin_sync(), blender::ed::sculpt_paint::brushes::clay_strips::calc_local_matrix(), blender::nodes::node_fn_combine_transform_cc::CombineTransformFunction::call(), chromatic_adaption_matrix(), blender::nodes::node_geo_string_to_curves_cc::create_curve_instances(), blender::ed::sculpt_paint::brushes::do_clay_thumb_brush(), blender::ed::sculpt_paint::brushes::do_plane_brush(), drw_shgroup_bone_custom_empty(), blender::draw::drw_volume_object_mesh_init(), blender::nodes::node_composite_scale_cc::ScaleOperation::execute_constant_size(), from_loc_scale(), from_rot_scale(), blender::math::detail::from_rotation(), blender::bke::greasepencil::convert::get_legacy_stroke_to_texture_matrix(), blender::get_mirror_matrix(), blender::bke::greasepencil::get_stroke_to_texture_matrix(), blender::ed::greasepencil::grease_pencil_texture_gradient_exec(), blender::draw::overlay::Bounds::object_sync(), polar_decompose(), pseudo_invert(), blender::eevee::PlanarProbe::set_view(), blender::eevee::VolumeProbeModule::set_view(), blender::tests::TEST(), blender::tests::TEST(), blender::draw::test_draw_manager_sync(), blender::draw::test_draw_resource_id_gen(), blender::draw::test_draw_visibility(), blender::imbuf::tests::transform_2x_smaller(), blender::imbuf::tests::transform_fractional_larger(), blender::ed::view3d::geometry_nodes_gizmos::TransformGizmos::update_scale_transform_and_target_property(), and blender::ed::view3d::geometry_nodes_gizmos::DialGizmo::update_transform().

◆ from_tracking()

template<typename T>

QuaternionBase< T > blender::math::from_tracking	(	AxisSigned	forward_axis,
		Axis	up_axis )

nodiscard

Returns a quaternion for converting local space to tracking space. This is slightly different than from_axis_conversion for legacy reasons.

Definition at line 351 of file BLI_math_rotation.hh.

References blender::math::AxisSigned::axis(), BLI_assert, from_orthonormal_axes(), rotation_between(), blender::math::AxisSigned::Y_POS, and blender::math::AxisSigned::Z_POS.

◆ from_triangle() [1/2]

template<typename T>

QuaternionBase< T > blender::math::from_triangle	(	const VecBase< T, 3 > &	v1,
		const VecBase< T, 3 > &	v2,
		const VecBase< T, 3 > &	v3 )

nodiscard

Create a orientation from a triangle plane and the axis formed by the segment(v1, v2).

Definition at line 261 of file BLI_math_rotation.hh.

References from_triangle(), normal_tri(), and v2.

◆ from_triangle() [2/2]

template<typename T>

QuaternionBase< T > blender::math::from_triangle	(	const VecBase< T, 3 > &	v1,
		const VecBase< T, 3 > &	v2,
		const VecBase< T, 3 > &	v3,
		const VecBase< T, 3 > &	normal )

nodiscard

Create a orientation from a triangle plane and the axis formed by the segment(v1, v2). Takes pre-computed normal from the triangle. Used for Ngons when their normal is known.

Definition at line 227 of file BLI_math_rotation.hh.

References angle(), atan2(), conjugate(), cos(), is_zero(), nor, normalize, safe_acos(), sin(), T, transform_point(), UNUSED_VARS, and v2.

Referenced by from_triangle(), and blender::math::tests::TEST().

◆ from_up_axis()

template<typename MatT, typename VectorT>

MatT blender::math::from_up_axis ( const VectorT up )

nodiscard

Create a rotation matrix from only one up axis. The other axes are chosen to always be orthogonal. The resulting matrix is a basis matrix.

Note: up must be normalized.; This can be used to create a tangent basis from a normal vector.; The output of this function is not given to be same across blender version. Prefer using from_orthonormal_axes for more stable output.

Definition at line 1511 of file BLI_math_matrix.hh.

References b, BLI_assert, is_unit_scale(), sign(), square(), T, blender::MatBase< T, NumCol, NumRow, Alignment >::x_axis(), blender::MatBase< T, NumCol, NumRow, Alignment >::y_axis(), and blender::MatBase< T, NumCol, NumRow, Alignment >::z_axis().

Referenced by blender::tests::TEST().

◆ from_vector()

template<typename T>

QuaternionBase< T > blender::math::from_vector	(	const VecBase< T, 3 > &	vector,
		const AxisSigned	track_flag,
		const Axis	up_flag )

nodiscard

Create a rotation from a vector and a basis rotation. Used for tracking. track_flag is supposed to be Object.trackflag up_flag is supposed to be Object.upflag

Definition at line 269 of file BLI_math_rotation.hh.

References angle(), blender::math::Axis::as_int(), blender::math::AxisSigned::axis(), blender::math::AngleCartesianBase< T >::cos(), cross(), e, eps, blender::math::QuaternionBase< T >::identity(), blender::math::AxisSigned::is_negative(), length(), normalize, normalize_and_get_length(), safe_acos(), blender::math::AngleCartesianBase< T >::sin(), T, to_quaternion(), transform_point(), UNLIKELY, blender::math::Axis::X, blender::math::Axis::Y, and blender::math::Axis::Z.

Referenced by blender::math::tests::TEST().

◆ half_to_float()

float blender::math::half_to_float ( uint16_t v )

Converts half-precision (FP16) number to float (FP32).

Definition at line 108 of file math_half.cc.

References exp(), magic(), and v.

Referenced by blender::gpu::convert(), blender::gpu::convert(), half_to_float_array(), ViewportColorSampleSession::sample(), and blender::tests::TEST().

◆ half_to_float_array()

void blender::math::half_to_float_array	(	const uint16_t *	src,
		float *	dst,
		size_t	length )

Definition at line 368 of file math_half.cc.

References half_to_float(), i, and length().

Referenced by blender::gpu::convert_buffer(), and blender::tests::TEST().

◆ hypot()

template<typename T>

T blender::math::hypot	(	const T &	y,
		const T &	x )

inline

Definition at line 268 of file BLI_math_base.hh.

References T, x, and y.

Referenced by blender::math::detail::normalized_to_eul2(), and blender::math::detail::normalized_to_eul2().

◆ interpolate() [1/11]

template<eAlpha Alpha>

ColorSceneLinear4f< Alpha > blender::math::interpolate	(	const ColorSceneLinear4f< Alpha > &	a,
		const ColorSceneLinear4f< Alpha > &	b,
		const float	t )

inline

Definition at line 18 of file BLI_math_color.hh.

References blender::ColorRGBA< ChannelStorageType, Space, Alpha >::a, b, blender::ColorRGBA< ChannelStorageType, Space, Alpha >::b, blender::ColorRGBA< ChannelStorageType, Space, Alpha >::g, interpolate(), and blender::ColorRGBA< ChannelStorageType, Space, Alpha >::r.

◆ interpolate() [2/11]

template<eAlpha Alpha>

ColorSceneLinearByteEncoded4b< Alpha > blender::math::interpolate	(	const ColorSceneLinearByteEncoded4b< Alpha > &	a,
		const ColorSceneLinearByteEncoded4b< Alpha > &	b,
		const float	t )

inline

Definition at line 29 of file BLI_math_color.hh.

References blender::ColorRGBA< ChannelStorageType, Space, Alpha >::a, b, blender::ColorRGBA< ChannelStorageType, Space, Alpha >::b, blender::ColorRGBA< ChannelStorageType, Space, Alpha >::g, interpolate(), and blender::ColorRGBA< ChannelStorageType, Space, Alpha >::r.

◆ interpolate() [3/11]

template double3x3 blender::math::interpolate	(	const double3x3 &	a,
		const double3x3 &	b,
		double	t )

References b, and interpolate().

◆ interpolate() [4/11]

template double4x4 blender::math::interpolate	(	const double4x4 &	a,
		const double4x4 &	b,
		double	t )

References b, and interpolate().

◆ interpolate() [5/11]

template float3x3 blender::math::interpolate	(	const float3x3 &	a,
		const float3x3 &	b,
		float	t )

References b, and interpolate().

◆ interpolate() [6/11]

template float4x4 blender::math::interpolate	(	const float4x4 &	a,
		const float4x4 &	b,
		float	t )

References b, and interpolate().

◆ interpolate() [7/11]

template<typename T>

MatBase< T, 3, 3 > blender::math::interpolate	(	const MatBase< T, 3, 3 > &	a,
		const MatBase< T, 3, 3 > &	b,
		T	t )

nodiscard

A polar-decomposition-based interpolation between matrix A and matrix B.

Note: This code is about five times slower than the 'naive' interpolation (it typically remains below 2 usec on an average i74700, while naive implementation remains below 0.4 usec). However, it gives expected results even with non-uniformly scaled matrices, see #46418 for an example.

Based on "Matrix Animation and Polar Decomposition", by Ken Shoemake & Tom Duff

Parameters

A	Input matrix which is totally effective with t = 0.0.
B	Input matrix which is totally effective with t = 1.0.
t	Interpolation factor.

Definition at line 336 of file math_matrix.cc.

References A, B, from_rotation(), interpolate(), interpolate_linear(), is_negative(), normalize, P, polar_decompose(), T, to_quaternion(), and U.

◆ interpolate() [8/11]

template<typename T>

MatBase< T, 4, 4 > blender::math::interpolate	(	const MatBase< T, 4, 4 > &	a,
		const MatBase< T, 4, 4 > &	b,
		T	t )

nodiscard

Complete transform matrix interpolation, based on polar-decomposition-based interpolation from interpolate<T, 3, 3>.

Parameters

A	Input matrix which is totally effective with t = 0.0.
B	Input matrix which is totally effective with t = 1.0.
t	Interpolation factor.

Definition at line 380 of file math_matrix.cc.

References A, B, interpolate(), result, and T.

◆ interpolate() [9/11]

template<typename T>

QuaternionBase< T > blender::math::interpolate	(	const QuaternionBase< T > &	a,
		const QuaternionBase< T > &	b,
		T	t )

inlinenodiscard

Use spherical interpolation between two quaternions. Always interpolate along the shortest angle.

Definition at line 301 of file BLI_math_quaternion.hh.

References b, BLI_assert, dot(), interpolate_dot_slerp(), is_unit_scale(), T, and w().

◆ interpolate() [10/11]

template<typename T, typename FactorT>

T blender::math::interpolate	(	const T &	a,
		const T &	b,
		const FactorT &	t )

inline

Definition at line 274 of file BLI_math_base.hh.

References b, result, and T.

◆ interpolate() [11/11]

template<typename T, typename FactorT, int Size>

VecBase< T, Size > blender::math::interpolate	(	const VecBase< T, Size > &	a,
		const VecBase< T, Size > &	b,
		const FactorT &	t )

inlinenodiscard

Per component linear interpolation.

Parameters

t	interpolation factor. Return a if equal 0. Return b if equal 1. Outside of [0..1] range, use linear extrapolation.

Definition at line 631 of file BLI_math_vector.hh.

References b.

◆ interpolate_bilinear_border_byte()

uchar4 blender::math::interpolate_bilinear_border_byte	(	const uchar *	buffer,
		int	width,
		int	height,
		float	u,
		float	v )

nodiscard

Bilinear sampling (with black border).

Takes four image samples at floor(u,v) and floor(u,v)+1, and blends them based on fractional parts of u,v. Samples outside the image are turned into transparent black.

Note that you probably want to subtract 0.5 from u,v before this function, to get proper filtering.

Definition at line 561 of file math_interp.cc.

References bilinear_byte_impl(), and v.

Referenced by blender::seq::MaskSamplerTransformedByte::apply_mask(), blender::imbuf::interpolate_bilinear_border_byte(), blender::imbuf::interpolate_bilinear_border_byte(), blender::seq::MaskSamplerTransformedByte::load_mask_min(), TEST(), TEST(), TEST(), TEST(), TEST(), and TEST().

◆ interpolate_bilinear_border_fl() [1/2]

void blender::math::interpolate_bilinear_border_fl	(	const float *	buffer,
		float *	output,
		int	width,
		int	height,
		int	components,
		float	u,
		float	v )

Definition at line 580 of file math_interp.cc.

References bilinear_fl_impl(), Border, output, and v.

◆ interpolate_bilinear_border_fl() [2/2]

float4 blender::math::interpolate_bilinear_border_fl	(	const float *	buffer,
		int	width,
		int	height,
		float	u,
		float	v )

nodiscard

Definition at line 572 of file math_interp.cc.

References bilinear_fl_impl(), Border, and v.

Referenced by blender::seq::MaskSamplerTransformedFloat::apply_mask(), blender::imbuf::interpolate_bilinear_border_fl(), blender::imbuf::interpolate_bilinear_border_fl(), blender::seq::MaskSamplerTransformedFloat::load_mask_min(), blender::compositor::Result::sample_bilinear_zero(), TEST(), TEST(), and TEST().

◆ interpolate_bilinear_byte()

uchar4 blender::math::interpolate_bilinear_byte	(	const uchar *	buffer,
		int	width,
		int	height,
		float	u,
		float	v )

nodiscard

Bilinear sampling.

Takes four image samples at floor(u,v) and floor(u,v)+1, and blends them based on fractional parts of u,v. Samples outside the image are clamped to texels at image edge.

Note that you probably want to subtract 0.5 from u,v before this function, to get proper filtering.

Definition at line 567 of file math_interp.cc.

References bilinear_byte_impl(), and v.

Referenced by blender::imbuf::interpolate_bilinear_byte(), blender::imbuf::interpolate_bilinear_byte(), and TEST().

◆ interpolate_bilinear_fl() [1/2]

void blender::math::interpolate_bilinear_fl	(	const float *	buffer,
		float *	output,
		int	width,
		int	height,
		int	components,
		float	u,
		float	v )

Definition at line 602 of file math_interp.cc.

References bilinear_fl_impl(), Extend, output, and v.

◆ interpolate_bilinear_fl() [2/2]

float4 blender::math::interpolate_bilinear_fl	(	const float *	buffer,
		int	width,
		int	height,
		float	u,
		float	v )

nodiscard

Definition at line 594 of file math_interp.cc.

References bilinear_fl_impl(), Extend, and v.

Referenced by blender::imbuf::interpolate_bilinear_fl(), blender::imbuf::interpolate_bilinear_fl(), blender::compositor::Result::sample_bilinear_extended(), blender::imbuf::transform::sample_image(), scale_bilinear_func(), and TEST().

◆ interpolate_bilinear_wrap_byte()

uchar4 blender::math::interpolate_bilinear_wrap_byte	(	const uchar *	buffer,
		int	width,
		int	height,
		float	u,
		float	v )

nodiscard

Wrapped bilinear sampling. (u,v) is repeated to be inside the image size, including properly wrapping samples that are right on the edges.

Definition at line 629 of file math_interp.cc.

References b, BLI_assert, floored_fmod(), floorf, and v.

Referenced by blender::imbuf::interpolate_bilinear_wrap_byte(), and TEST().

◆ interpolate_bilinear_wrap_fl()

float4 blender::math::interpolate_bilinear_wrap_fl	(	const float *	buffer,
		int	width,
		int	height,
		float	u,
		float	v )

nodiscard

Definition at line 671 of file math_interp.cc.

References bilinear_fl_impl(), Repeat, and v.

Referenced by blender::imbuf::interpolate_bilinear_wrap_fl(), and TEST().

◆ interpolate_bilinear_wrapmode_fl()

void blender::math::interpolate_bilinear_wrapmode_fl	(	const float *	buffer,
		float *	output,
		int	width,
		int	height,
		int	components,
		float	u,
		float	v,
		InterpWrapMode	wrap_u,
		InterpWrapMode	wrap_v )

Definition at line 616 of file math_interp.cc.

References bilinear_fl_impl(), output, and v.

Referenced by blender::compositor::Result::sample(), blender::compositor::Result::sample_bilinear_wrap(), blender::imbuf::transform::sample_image(), and TEST().

◆ interpolate_cubic_bspline_byte()

uchar4 blender::math::interpolate_cubic_bspline_byte	(	const uchar *	buffer,
		int	width,
		int	height,
		float	u,
		float	v )

nodiscard

Cubic B-Spline sampling.

Takes 4x4 image samples at floor(u,v)-1 .. floor(u,v)+2, and blends them based on fractional parts of u,v. Uses B-Spline variant Mitchell-Netravali filter (B=1, C=0), which has no ringing but introduces quite a lot of blur. Samples outside the image are clamped to texels at image edge.

Note that you probably want to subtract 0.5 from u,v before this function, to get proper filtering.

Definition at line 679 of file math_interp.cc.

References bicubic_interpolation(), Extend, and v.

Referenced by blender::imbuf::interpolate_cubic_bspline_byte(), blender::imbuf::interpolate_cubic_bspline_byte(), TEST(), TEST(), and TEST().

◆ interpolate_cubic_bspline_fl() [1/2]

void blender::math::interpolate_cubic_bspline_fl	(	const float *	buffer,
		float *	output,
		int	width,
		int	height,
		int	components,
		float	u,
		float	v )

Definition at line 695 of file math_interp.cc.

References bicubic_interpolation(), Extend, output, and v.

◆ interpolate_cubic_bspline_fl() [2/2]

float4 blender::math::interpolate_cubic_bspline_fl	(	const float *	buffer,
		int	width,
		int	height,
		float	u,
		float	v )

nodiscard

Definition at line 687 of file math_interp.cc.

References bicubic_interpolation(), Extend, and v.

Referenced by blender::imbuf::interpolate_cubic_bspline_fl(), blender::imbuf::interpolate_cubic_bspline_fl(), blender::compositor::Result::sample_cubic_extended(), blender::imbuf::transform::sample_image(), TEST(), and TEST().

◆ interpolate_cubic_bspline_wrapmode_fl()

void blender::math::interpolate_cubic_bspline_wrapmode_fl	(	const float *	buffer,
		float *	output,
		int	width,
		int	height,
		int	components,
		float	u,
		float	v,
		math::InterpWrapMode	wrap_u,
		math::InterpWrapMode	wrap_v )

Definition at line 709 of file math_interp.cc.

References bicubic_interpolation(), output, and v.

Referenced by blender::compositor::Result::sample(), blender::compositor::Result::sample_cubic_wrap(), and TEST().

◆ interpolate_cubic_mitchell_byte()

uchar4 blender::math::interpolate_cubic_mitchell_byte	(	const uchar *	buffer,
		int	width,
		int	height,
		float	u,
		float	v )

nodiscard

Cubic Mitchell sampling.

Takes 4x4 image samples at floor(u,v)-1 .. floor(u,v)+2, and blends them based on fractional parts of u,v. Uses Mitchell-Netravali filter (B=C=1/3), which has a good compromise between blur and ringing. Samples outside the image are clamped to texels at image edge.

Note that you probably want to subtract 0.5 from u,v before this function, to get proper filtering.

Definition at line 723 of file math_interp.cc.

References bicubic_interpolation(), Extend, and v.

Referenced by blender::imbuf::interpolate_cubic_mitchell_byte(), blender::imbuf::interpolate_cubic_mitchell_byte(), TEST(), TEST(), and TEST().

◆ interpolate_cubic_mitchell_fl() [1/2]

void blender::math::interpolate_cubic_mitchell_fl	(	const float *	buffer,
		float *	output,
		int	width,
		int	height,
		int	components,
		float	u,
		float	v )

Definition at line 740 of file math_interp.cc.

References bicubic_interpolation(), Extend, output, and v.

◆ interpolate_cubic_mitchell_fl() [2/2]

float4 blender::math::interpolate_cubic_mitchell_fl	(	const float *	buffer,
		int	width,
		int	height,
		float	u,
		float	v )

nodiscard

Definition at line 732 of file math_interp.cc.

References bicubic_interpolation(), Extend, and v.

Referenced by blender::imbuf::transform::sample_image(), TEST(), and TEST().

◆ interpolate_dot_slerp()

template<typename T>

VecBase< T, 2 > blender::math::interpolate_dot_slerp	(	const T	t,
		const T	cosom )

inlinenodiscard

Generic function for implementing slerp (quaternions and spherical vector coords).

Parameters

t	factor in [0..1]
cosom	dot product from normalized quaternions.

Returns: calculated weights.

Definition at line 271 of file BLI_math_quaternion.hh.

References abs(), acos(), BLI_assert, e, eps, IN_RANGE_INCL, LIKELY, sin(), T, and w().

Referenced by interpolate().

◆ interpolate_fast() [1/6]

template double3x3 blender::math::interpolate_fast	(	const double3x3 &	a,
		const double3x3 &	b,
		double	t )

References b, and interpolate_fast().

◆ interpolate_fast() [2/6]

template double4x4 blender::math::interpolate_fast	(	const double4x4 &	a,
		const double4x4 &	b,
		double	t )

References b, and interpolate_fast().

◆ interpolate_fast() [3/6]

template float3x3 blender::math::interpolate_fast	(	const float3x3 &	a,
		const float3x3 &	b,
		float	t )

References b, and interpolate_fast().

◆ interpolate_fast() [4/6]

template float4x4 blender::math::interpolate_fast	(	const float4x4 &	a,
		const float4x4 &	b,
		float	t )

References b, and interpolate_fast().

◆ interpolate_fast() [5/6]

template<typename T>

MatBase< T, 3, 3 > blender::math::interpolate_fast	(	const MatBase< T, 3, 3 > &	a,
		const MatBase< T, 3, 3 > &	b,
		T	t )

nodiscard

Naive interpolation implementation, faster than polar decomposition

Note: This code is about five times faster than the polar decomposition. However, it gives un-expected results even with non-uniformly scaled matrices, see #46418 for an example.

Parameters

A	Input matrix which is totally effective with t = 0.0.
B	Input matrix which is totally effective with t = 1.0.
t	Interpolation factor.

Definition at line 397 of file math_matrix.cc.

References b, from_rot_scale(), interpolate(), interpolate_fast(), scale(), T, and to_rot_scale().

Referenced by interpolate_fast(), interpolate_fast(), interpolate_fast(), interpolate_fast(), interpolate_fast(), interpolate_fast(), blender::tests::TEST(), and blender::tests::TEST().

◆ interpolate_fast() [6/6]

template<typename T>

MatBase< T, 4, 4 > blender::math::interpolate_fast	(	const MatBase< T, 4, 4 > &	a,
		const MatBase< T, 4, 4 > &	b,
		T	t )

nodiscard

Naive transform matrix interpolation, based on naive-decomposition-based interpolation from interpolate_fast<T, 3, 3>.

Note: This code is about five times faster than the polar decomposition. However, it gives un-expected results even with non-uniformly scaled matrices, see #46418 for an example.

Parameters

A	Input matrix which is totally effective with t = 0.0.
B	Input matrix which is totally effective with t = 1.0.
t	Interpolation factor.

Definition at line 416 of file math_matrix.cc.

References b, from_loc_rot_scale(), interpolate(), interpolate_fast(), scale(), T, and to_loc_rot_scale().

◆ interpolate_linear()

template<typename T, int NumCol, int NumRow>

MatBase< T, NumCol, NumRow > blender::math::interpolate_linear	(	const MatBase< T, NumCol, NumRow > &	a,
		const MatBase< T, NumCol, NumRow > &	b,
		T	t )

nodiscard

Interpolate each component linearly.

Definition at line 730 of file BLI_math_matrix.hh.

References b, interpolate(), result, T, and blender::unroll().

Referenced by interpolate().

◆ interpolate_nearest_border_byte() [1/2]

uchar4 blender::math::interpolate_nearest_border_byte	(	const uchar *	buffer,
		int	width,
		int	height,
		float	u,
		float	v )

inlinenodiscard

Definition at line 77 of file BLI_math_interp.hh.

References interpolate_nearest_border_byte(), and v.

◆ interpolate_nearest_border_byte() [2/2]

void blender::math::interpolate_nearest_border_byte	(	const uchar *	buffer,
		uchar *	output,
		int	width,
		int	height,
		float	u,
		float	v )

inline

Nearest (point) sampling (with black border).

Returns texel at floor(u,v) integer index. Samples outside the image are turned into transparent black.

Note that it is not "nearest to u,v coordinate", but rather with fractional part truncated (it would be "nearest" if subtracting 0.5 from input u,v).

Definition at line 57 of file BLI_math_interp.hh.

References BLI_assert, data, output, v, x, and y.

Referenced by blender::imbuf::interpolate_nearest_border_byte(), blender::imbuf::interpolate_nearest_border_byte(), interpolate_nearest_border_byte(), TEST(), and TEST().

◆ interpolate_nearest_border_fl() [1/2]

void blender::math::interpolate_nearest_border_fl	(	const float *	buffer,
		float *	output,
		int	width,
		int	height,
		int	components,
		float	u,
		float	v )

inline

Definition at line 85 of file BLI_math_interp.hh.

References BLI_assert, data, i, output, v, x, and y.

Referenced by blender::imbuf::interpolate_nearest_border_fl(), blender::imbuf::interpolate_nearest_border_fl(), interpolate_nearest_border_fl(), blender::imbuf::transform::sample_image(), blender::compositor::Result::sample_nearest_zero(), TEST(), and TEST().

◆ interpolate_nearest_border_fl() [2/2]

float4 blender::math::interpolate_nearest_border_fl	(	const float *	buffer,
		int	width,
		int	height,
		float	u,
		float	v )

inlinenodiscard

Definition at line 106 of file BLI_math_interp.hh.

References interpolate_nearest_border_fl(), and v.

◆ interpolate_nearest_byte() [1/2]

uchar4 blender::math::interpolate_nearest_byte	(	const uchar *	buffer,
		int	width,
		int	height,
		float	u,
		float	v )

inlinenodiscard

Definition at line 138 of file BLI_math_interp.hh.

References interpolate_nearest_byte(), and v.

◆ interpolate_nearest_byte() [2/2]

void blender::math::interpolate_nearest_byte	(	const uchar *	buffer,
		uchar *	output,
		int	width,
		int	height,
		float	u,
		float	v )

inline

Nearest (point) sampling.

Returns texel at floor(u,v) integer index. Samples outside the image are clamped to texels at image edge.

Note that it is not "nearest to u,v coordinate", but rather with fractional part truncated (it would be "nearest" if subtracting 0.5 from input u,v).

Definition at line 124 of file BLI_math_interp.hh.

References BLI_assert, clamp(), data, output, v, x, and y.

Referenced by interpolate_nearest_byte().

◆ interpolate_nearest_fl() [1/2]

void blender::math::interpolate_nearest_fl	(	const float *	buffer,
		float *	output,
		int	width,
		int	height,
		int	components,
		float	u,
		float	v )

inline

Definition at line 146 of file BLI_math_interp.hh.

References BLI_assert, clamp(), data, i, output, v, x, and y.

Referenced by interpolate_nearest_fl(), and blender::compositor::Result::sample_nearest_extended().

◆ interpolate_nearest_fl() [2/2]

float4 blender::math::interpolate_nearest_fl	(	const float *	buffer,
		int	width,
		int	height,
		float	u,
		float	v )

inlinenodiscard

Definition at line 159 of file BLI_math_interp.hh.

References interpolate_nearest_fl(), and v.

◆ interpolate_nearest_wrap_byte() [1/2]

uchar4 blender::math::interpolate_nearest_wrap_byte	(	const uchar *	buffer,
		int	width,
		int	height,
		float	u,
		float	v )

inlinenodiscard

Definition at line 188 of file BLI_math_interp.hh.

References interpolate_nearest_wrap_byte(), and v.

◆ interpolate_nearest_wrap_byte() [2/2]

void blender::math::interpolate_nearest_wrap_byte	(	const uchar *	buffer,
		uchar *	output,
		int	width,
		int	height,
		float	u,
		float	v )

inline

Wrapped nearest sampling. (u,v) is repeated to be inside the image size.

Definition at line 171 of file BLI_math_interp.hh.

References BLI_assert, data, floored_fmod(), output, v, x, and y.

Referenced by blender::imbuf::interpolate_nearest_wrap_byte(), and interpolate_nearest_wrap_byte().

◆ interpolate_nearest_wrap_fl() [1/2]

void blender::math::interpolate_nearest_wrap_fl	(	const float *	buffer,
		float *	output,
		int	width,
		int	height,
		int	components,
		float	u,
		float	v )

inline

Definition at line 196 of file BLI_math_interp.hh.

References BLI_assert, data, floored_fmod(), i, output, v, x, and y.

Referenced by blender::imbuf::interpolate_nearest_wrap_fl(), and interpolate_nearest_wrap_fl().

◆ interpolate_nearest_wrap_fl() [2/2]

float4 blender::math::interpolate_nearest_wrap_fl	(	const float *	buffer,
		int	width,
		int	height,
		float	u,
		float	v )

inlinenodiscard

Definition at line 212 of file BLI_math_interp.hh.

References interpolate_nearest_wrap_fl(), and v.

◆ interpolate_nearest_wrapmode_fl()

void blender::math::interpolate_nearest_wrapmode_fl	(	const float *	buffer,
		float *	output,
		int	width,
		int	height,
		int	components,
		float	u,
		float	v,
		InterpWrapMode	wrap_u,
		InterpWrapMode	wrap_v )

Definition at line 43 of file math_interp.cc.

References BLI_assert, data, i, output, v, wrap_coord(), x, and y.

Referenced by blender::compositor::Result::sample(), and blender::compositor::Result::sample_nearest_wrap().

◆ invert() [1/10]

CartesianBasis blender::math::invert ( const CartesianBasis & basis )

inlinenodiscard

Return the inverse transformation represented by the given basis. This is conceptually the equivalent to a rotation matrix transpose, but much faster.

Definition at line 460 of file BLI_math_basis_types.hh.

References blender::math::AxisSigned::axis(), blender::math::AxisSigned::is_negative(), result, blender::math::Axis::X, blender::math::CartesianBasis::x(), blender::math::AxisSigned::X_NEG, blender::math::AxisSigned::X_POS, blender::math::Axis::Y, blender::math::CartesianBasis::y(), blender::math::AxisSigned::Y_NEG, blender::math::AxisSigned::Y_POS, blender::math::Axis::Z, blender::math::CartesianBasis::z(), blender::math::AxisSigned::Z_NEG, and blender::math::AxisSigned::Z_POS.

◆ invert() [2/10]

template double2x2 blender::math::invert	(	const double2x2 &	mat,
		bool &	r_success )

◆ invert() [3/10]

template double3x3 blender::math::invert	(	const double3x3 &	mat,
		bool &	r_success )

◆ invert() [4/10]

template double4x4 blender::math::invert	(	const double4x4 &	mat,
		bool &	r_success )

◆ invert() [5/10]

template float2x2 blender::math::invert	(	const float2x2 &	mat,
		bool &	r_success )

◆ invert() [6/10]

template float3x3 blender::math::invert	(	const float3x3 &	mat,
		bool &	r_success )

◆ invert() [7/10]

template float4x4 blender::math::invert	(	const float4x4 &	mat,
		bool &	r_success )

◆ invert() [8/10]

template<typename T, int Size>

MatBase< T, Size, Size > blender::math::invert ( const MatBase< T, Size, Size > & mat )

nodiscard

Definition at line 643 of file BLI_math_matrix.hh.

References invert().

◆ invert() [9/10]

template<typename T, int Size>

MatBase< T, Size, Size > blender::math::invert	(	const MatBase< T, Size, Size > &	mat,
		bool &	r_success )

nodiscard

Returns the inverse of a square matrix or zero matrix on failure. r_success is optional and set to true if the matrix was inverted successfully.

Definition at line 203 of file math_matrix.cc.

References blender::MatBase< T, NumCol, NumRow, Alignment >::base_ptr(), M, R, and result.

◆ invert() [10/10]

template<typename T>

QuaternionBase< T > blender::math::invert ( const QuaternionBase< T > & q )

inlinenodiscard

Return invert of q or identity if q is ill-formed. The invert allows quaternion division.

Note: The inverse of q isn't the opposite rotation. This would be the conjugate.

Definition at line 232 of file BLI_math_quaternion.hh.

References conjugate(), dot(), blender::math::QuaternionBase< T >::identity(), length_squared(), and T.

◆ invert_normalized()

template<typename T>

QuaternionBase< T > blender::math::invert_normalized ( const QuaternionBase< T > & q )

inlinenodiscard

Return invert of q assuming it is a unit quaternion. In this case, the inverse is just the conjugate. conjugate(q) could be use directly, but this function shows the intent better, and asserts if q ever becomes non-unit-length.

Definition at line 242 of file BLI_math_quaternion.hh.

References BLI_assert, conjugate(), and is_unit_scale().

Referenced by blender::math::QuaternionBase< T >::swing(), blender::math::tests::TEST(), and blender::math::QuaternionBase< T >::wrapped_around().

◆ is_any_zero() [1/2]

template<typename T>

bool blender::math::is_any_zero ( const T & a )

inline

Definition at line 28 of file BLI_math_base.hh.

References is_zero(), and T.

Referenced by blender::nodes::node_composite_ellipsemask_cc::EllipseMaskOperation::execute(), and blender::ed::space_node::node_gizmo_safe_calc_dims().

◆ is_any_zero() [2/2]

template<typename T, int Size>

bool blender::math::is_any_zero ( const VecBase< T, Size > & a )

inlinenodiscard

Returns true if at least one component is exactly equal to 0.

Definition at line 792 of file BLI_math_vector.hh.

References i, and T.

◆ is_equal() [1/3]

template<typename T, int NumCol, int NumRow>

bool blender::math::is_equal	(	const MatBase< T, NumCol, NumRow > &	a,
		const MatBase< T, NumCol, NumRow > &	b,
		const T	epsilon = T(0) )

inlinenodiscard

Returns true if matrices are equal within the given epsilon.

Definition at line 504 of file BLI_math_matrix.hh.

References abs(), b, i, and T.

Referenced by blender::bke::build_mesh_positions(), blender::nodes::node_fn_combine_transform_cc::CombineTransformFunction::call(), colormanage_update_matrices(), blender::compositor::RealizeOnDomainOperation::compute_realized_transformation_domain(), blender::bke::subdiv::eval_limit_point_and_derivatives(), blender::nodes::node_composite_despeckle_cc::DespeckleOperation::execute_cpu(), IMB_colormanagement_working_space_convert(), imb_colormanagement_working_space_set_from_matrix(), SELECTID_Context::is_dirty(), blender::compositor::Domain::is_equal(), blender::geometry::skip_transform(), skip_transform(), blender::tests::TEST(), blender::tests::TEST(), transform_normals(), and transform_normals().

◆ is_equal() [2/3]

template<typename T>

bool blender::math::is_equal	(	const QuaternionBase< T > &	a,
		const QuaternionBase< T > &	b,
		const T	epsilon = T(0) )

inlinenodiscard

Returns true if the quaternions are equal within the given epsilon. Return false otherwise.

Definition at line 115 of file BLI_math_quaternion.hh.

References abs(), b, T, blender::math::QuaternionBase< T >::w, blender::math::QuaternionBase< T >::x, blender::math::QuaternionBase< T >::y, and blender::math::QuaternionBase< T >::z.

◆ is_equal() [3/3]

template<typename T, int Size>

bool blender::math::is_equal	(	const VecBase< T, Size > &	a,
		const VecBase< T, Size > &	b,
		const T	epsilon = T(0) )

inlinenodiscard

Returns true if vectors are equal within the given epsilon.

Definition at line 760 of file BLI_math_vector.hh.

References abs(), b, i, and T.

◆ is_identity()

template<typename T, int NumCol, int NumRow>

bool blender::math::is_identity ( const MatBase< T, NumCol, NumRow > & mat )

inlinenodiscard

Returns true if the matrix is exactly the identity matrix.

Definition at line 522 of file BLI_math_matrix.hh.

References i.

Referenced by blender::seq::apply_modifier_op().

◆ is_negative() [1/6]

template bool blender::math::is_negative ( const double3x3 & mat )

References is_negative().

◆ is_negative() [2/6]

template bool blender::math::is_negative ( const double4x4 & mat )

References is_negative().

◆ is_negative() [3/6]

template bool blender::math::is_negative ( const float3x3 & mat )

References is_negative().

◆ is_negative() [4/6]

template bool blender::math::is_negative ( const float4x4 & mat )

References is_negative().

◆ is_negative() [5/6]

template<typename T>

bool blender::math::is_negative ( const MatBase< T, 3, 3 > & mat )

nodiscard

Returns true if matrix has inverted handedness.

Note: It doesn't use determinant(mat4x4) as only the 3x3 components are needed assuming the matrix is used as a transformation to represent 3D location/scale/rotation.

Definition at line 143 of file math_matrix.cc.

References determinant(), is_negative(), and T.

Referenced by interpolate(), is_negative(), is_negative(), is_negative(), is_negative(), is_negative(), is_negative(), blender::geometry::boolean::mesh_bm_concat(), blender::math::detail::normalized_to_quat_fast(), blender::math::AngleFraction< T >::operator AngleCartesianBase< T >(), blender::math::AngleFraction< T >::radian(), blender::tests::TEST(), to_dual_quaternion(), to_rot_scale(), to_rot_scale(), to_scale(), and to_scale().

◆ is_negative() [6/6]

template<typename T>

bool blender::math::is_negative ( const MatBase< T, 4, 4 > & mat )

nodiscard

Definition at line 148 of file math_matrix.cc.

References blender::MatBase< T, NumCol, NumRow, Alignment >::base_ptr(), is_negative(), and T.

◆ is_normalized()

template<typename T>

bool blender::math::is_normalized ( const DualQuaternionBase< T > & dq )

inlinenodiscard

Returns true if the DualQuaternion has not been mixed with other DualQuaternion and needs no normalization.

Definition at line 286 of file BLI_math_quaternion_types.hh.

References blender::math::DualQuaternionBase< T >::quat_weight, and T.

Referenced by blender::draw::evaluate_vertex_weight(), blender::math::detail::from_rotation(), and transform_point().

◆ is_orthogonal()

template<typename MatT>

bool blender::math::is_orthogonal ( const MatT & mat )

inlinenodiscard

Test if the X, Y and Z axes are perpendicular with each other.

Definition at line 537 of file BLI_math_matrix.hh.

References abs(), and dot().

Referenced by is_orthonormal(), is_uniformly_scaled(), and blender::tests::TEST().

◆ is_orthonormal()

template<typename MatT>

bool blender::math::is_orthonormal ( const MatT & mat )

inlinenodiscard

Test if the X, Y and Z axes are perpendicular with each other and unit length.

Definition at line 554 of file BLI_math_matrix.hh.

References abs(), is_orthogonal(), and length_squared().

Referenced by blender::nodes::node_fn_axes_to_rotation_cc::AxesToRotationFunction::call(), blender::ed::view3d::geometry_nodes_gizmos::make_matrix_orthonormal_but_keep_z_axis(), blender::tests::TEST(), and to_dual_quaternion().

◆ is_similarity_transform()

template<typename T>

bool blender::math::is_similarity_transform	(	const MatBase< T, 3, 3 > &	matrix,
		const T &	epsilon = 1e-6 )

Check that each column is orthogonal to the others, and that each column is the same length. In other words, there is no shear, and any scaling is uniform.

Definition at line 526 of file math_matrix.cc.

References abs(), dot(), e, is_similarity_transform(), length_squared(), and T.

Referenced by is_similarity_transform(), transform_normals(), and transform_normals().

◆ is_uniformly_scaled()

template<typename MatT>

bool blender::math::is_uniformly_scaled ( const MatT & mat )

inlinenodiscard

Test if the X, Y and Z axes are perpendicular with each other and the same length.

Definition at line 574 of file BLI_math_matrix.hh.

References abs(), e, eps, is_orthogonal(), length_squared(), T, x, y, and z().

Referenced by blender::tests::TEST().

◆ is_unit()

template<typename T, int Size>

bool blender::math::is_unit	(	const VecBase< T, Size > &	a,
		const T	epsilon = T(10) * std::numeric_limits<T>::epsilon() )

inlinenodiscard

Return true if the squared length of the vector is (almost) equal to 1 (with a 10 * std::numeric_limits<T>::epsilon() epsilon error by default).

Definition at line 807 of file BLI_math_vector.hh.

References abs(), length(), length_squared(), and T.

Referenced by rotate_direction_around_axis().

◆ is_unit_scale() [1/3]

template<typename T, int NumCol, int NumRow>

bool blender::math::is_unit_scale ( const MatBase< T, NumCol, NumRow > & m )

inlinenodiscard

Definition at line 632 of file BLI_math_matrix.hh.

References i, and is_unit_scale().

Referenced by angle_between(), angle_of(), angle_of_signed(), blender::math::AxisAngleBase< T, AngleT >::AxisAngleBase(), blender::math::AxisAngleBase< T, AngleT >::AxisAngleBase(), blender::math::DualQuaternionBase< T >::DualQuaternionBase(), blender::math::DualQuaternionBase< T >::DualQuaternionBase(), blender::math::QuaternionBase< T >::expmap(), from_direction(), from_orthonormal_axes(), blender::math::detail::from_rotation(), from_up_axis(), interpolate(), invert_normalized(), is_unit_scale(), blender::ed::view3d::geometry_nodes_gizmos::matrix_from_position_and_up_direction(), blender::math::detail::normalized_to_angle(), blender::math::detail::normalized_to_eul2(), blender::math::detail::normalized_to_eul2(), blender::math::detail::normalized_to_quat_fast(), pow(), reflect(), blender::tests::TEST(), to_axis_angle(), to_euler(), to_euler(), to_quaternion(), transform_point(), and blender::math::QuaternionBase< T >::wrapped_around().

◆ is_unit_scale() [2/3]

template<typename T>

bool blender::math::is_unit_scale ( const QuaternionBase< T > & q )

inlinenodiscard

Definition at line 123 of file BLI_math_quaternion.hh.

References abs(), T, blender::math::QuaternionBase< T >::w, blender::math::QuaternionBase< T >::x, blender::math::QuaternionBase< T >::y, and blender::math::QuaternionBase< T >::z.

◆ is_unit_scale() [3/3]

template<typename T, int Size>

bool blender::math::is_unit_scale ( const VecBase< T, Size > & v )

inlinenodiscard

Return true if each individual column is unit scaled. Mainly for assert usage.

Definition at line 457 of file BLI_math_vector.hh.

References abs(), length_squared(), T, v, and blender::math::AssertUnitEpsilon< T >::value.

◆ is_zero() [1/4]

template<typename T, int NumCol, int NumRow>

bool blender::math::is_zero ( const MatBase< T, NumCol, NumRow > & mat )

inline

Definition at line 588 of file BLI_math_matrix.hh.

References i, and is_zero().

◆ is_zero() [2/4]

template<typename T>

bool blender::math::is_zero ( const QuaternionBase< T > & q )

inlinenodiscard

Returns true if all components are exactly equal to 0.

Definition at line 106 of file BLI_math_quaternion.hh.

References T, blender::math::QuaternionBase< T >::w, blender::math::QuaternionBase< T >::x, blender::math::QuaternionBase< T >::y, and blender::math::QuaternionBase< T >::z.

◆ is_zero() [3/4]

template<typename T>

bool blender::math::is_zero ( const T & a )

inline

Definition at line 23 of file BLI_math_base.hh.

References T.

◆ is_zero() [4/4]

template<typename T, int Size>

bool blender::math::is_zero	(	const VecBase< T, Size > &	a,
		const T	epsilon = T(0) )

inlinenodiscard

Return true if the absolute values of all components are smaller than given epsilon (0 by default).

Note: Does not compute the actual length of the vector, for performance.

Definition at line 779 of file BLI_math_vector.hh.

References abs(), i, and T.

◆ isect_seg_seg() [1/3]

template<>

isect_result< double2 > blender::math::isect_seg_seg	(	const double2 &	v1,
		const double2 &	v2,
		const double2 &	v3,
		const double2 &	v4 )

Definition at line 46 of file math_vec.cc.

References blender::math::isect_result< T >::kind, blender::math::isect_result< T >::lambda, blender::math::isect_result< T >::LINE_LINE_COLINEAR, blender::math::isect_result< T >::LINE_LINE_CROSS, blender::math::isect_result< T >::LINE_LINE_EXACT, blender::math::isect_result< T >::LINE_LINE_NONE, and v2.

◆ isect_seg_seg() [2/3]

template<>

isect_result< float2 > blender::math::isect_seg_seg	(	const float2 &	v1,
		const float2 &	v2,
		const float2 &	v3,
		const float2 &	v4 )

Definition at line 16 of file math_vec.cc.

References blender::math::isect_result< T >::kind, blender::math::isect_result< T >::lambda, blender::math::isect_result< T >::LINE_LINE_COLINEAR, blender::math::isect_result< T >::LINE_LINE_CROSS, blender::math::isect_result< T >::LINE_LINE_EXACT, blender::math::isect_result< T >::LINE_LINE_NONE, and v2.

◆ isect_seg_seg() [3/3]

template<typename T, int Size>

isect_result< VecBase< T, Size > > blender::math::isect_seg_seg	(	const VecBase< T, Size > &	v1,
		const VecBase< T, Size > &	v2,
		const VecBase< T, Size > &	v3,
		const VecBase< T, Size > &	v4 )

nodiscard

References v2.

Referenced by blender::meshintersect::fill_crossdata_for_intersect(), blender::ed::greasepencil::find_curve_intersections(), blender::ed::greasepencil::trim::get_intersections_of_curve_with_curves(), and blender::ed::sculpt_paint::grease_pencil_fill_extension_cut().

◆ length()

template<typename T, int Size>

T blender::math::length ( const VecBase< T, Size > & a )

inlinenodiscard

Definition at line 451 of file BLI_math_vector.hh.

References length_squared(), sqrt(), and T.

◆ length_manhattan()

template<typename T, int Size>

T blender::math::length_manhattan ( const VecBase< T, Size > & a )

inlinenodiscard

Returns summation of all components.

Definition at line 437 of file BLI_math_vector.hh.

References abs(), i, result, and T.

Referenced by apply_to_curves_point_selection(), distance_manhattan(), to_euler(), to_euler(), to_nearest_euler(), and to_nearest_euler().

◆ length_squared()

template<typename T, int Size>

T blender::math::length_squared ( const VecBase< T, Size > & a )

inlinenodiscard

Definition at line 446 of file BLI_math_vector.hh.

References dot(), and T.

◆ max() [1/4]

template<typename T>

T blender::math::max	(	const T &	a,
		const T &	b )

inline

Definition at line 49 of file BLI_math_base.hh.

References b, and T.

◆ max() [2/4]

template<typename T, int Size>

VecBase< T, Size > blender::math::max	(	const VecBase< T, Size > &	a,
		const VecBase< T, Size > &	b )

inlinenodiscard

Definition at line 88 of file BLI_math_vector.hh.

References b, BLI_UNROLL_MATH_VEC_FUNC_VEC_VEC, and max().

◆ max() [3/4]

template<typename T, int Size>

VecBase< T, Size > blender::math::max ( Span< VecBase< T, Size > > values )

inlinenodiscard

Element-wise maximum of the passed vectors.

Definition at line 97 of file BLI_math_vector.hh.

References BLI_assert, max, result, and v.

◆ max() [4/4]

template<typename T, int Size>

VecBase< T, Size > blender::math::max ( std::initializer_list< VecBase< T, Size > > values )

inlinenodiscard

Element-wise maximum of the passed vectors.

Definition at line 113 of file BLI_math_vector.hh.

References max.

◆ max_inplace()

template<typename T>

void blender::math::max_inplace	(	T &	a,
		const T &	b )

inline

Definition at line 55 of file BLI_math_base.hh.

References b, and T.

Referenced by blender::ed::sculpt_paint::PuffOperationExecutor::find_curve_weights_projected(), blender::ed::sculpt_paint::PuffOperationExecutor::find_curves_weights_spherical(), blender::ed::sculpt_paint::SmoothOperationExecutor::find_projected_smooth_factors(), blender::ed::sculpt_paint::SmoothOperationExecutor::find_spherical_smooth_factors(), UniqueName_Value::mark_used(), and blender::io::obj::Geometry::track_vertex_index().

◆ midpoint() [1/2]

template<typename T>

T blender::math::midpoint	(	const T &	a,
		const T &	b )

inline

See std::midpoint from C++20.

Definition at line 283 of file BLI_math_base.hh.

References b, sign(), and T.

Referenced by blender::bke::pbvh::build_nodes_recursive_grids(), blender::bke::pbvh::build_nodes_recursive_mesh(), blender::bke::calc_edge_centers(), blender::ed::sculpt_paint::filter::calc_sphere_translations(), blender::nodes::node_geo_field_average_cc::calculate_median(), blender::Bounds< T >::center(), blender::nodes::node_geo_curve_primitive_arc_cc::create_arc_curve_from_points(), blender::ed::sculpt_paint::brushes::do_multiplane_scrape_brush(), edbm_rip_edge_side_measure(), blender::ed::sculpt_paint::ensure_valid_pivot(), blender::ed::space_node::find_visible_center_of_link(), blender::nodes::node_geo_input_mesh_edge_angle_cc::SignedAngleFieldInput::get_varray_for_context(), blender::ed::greasepencil::grease_pencil_snap_cursor_to_sel_exec(), blender::bke::int2_to_int(), blender::ed::space_node::node_group_make_insert_selected(), blender::ed::object::object_origin_set_exec(), blender::draw::overlay::Bounds::object_sync(), paint_init_pivot_curves(), paint_init_pivot_grease_pencil(), paint_init_pivot_mesh(), blender::bke::partition_faces_recursively(), blender::bke::pbvh::pbvh_bmesh_node_limit_ensure_fast(), blender::bke::pbvh::pbvh_bmesh_node_split(), blender::bke::pbvh::pbvh_bmesh_split_edge(), blender::ed::sculpt_paint::dyntopo::sculpt_detail_flood_fill_exec(), blender::bke::short2_to_int(), blender::ed::sculpt_paint::SmoothOperationExecutor::smooth(), blender::eevee::IrradianceBake::surfel_raster_views_sync(), ObjectInfos::sync(), blender::tests::TEST(), blender::ed::transform::transform_mesh_edge_slide_data_create(), blender::ed::transform::transform_mesh_uv_edge_slide_data_create(), blender::draw::Manager::unique_handle_for_sculpt(), view3d_ob_drop_matrix_from_snap(), and view3d_orbit_calc_center().

◆ midpoint() [2/2]

template<typename T, int Size>

VecBase< T, Size > blender::math::midpoint	(	const VecBase< T, Size > &	a,
		const VecBase< T, Size > &	b )

inlinenodiscard

Returns: Point halfway between a and b.

Definition at line 642 of file BLI_math_vector.hh.

References b.

◆ min() [1/4]

template<typename T>

T blender::math::min	(	const T &	a,
		const T &	b )

inline

Definition at line 43 of file BLI_math_base.hh.

References b, and T.

◆ min() [2/4]

template<typename T, int Size>

VecBase< T, Size > blender::math::min	(	const VecBase< T, Size > &	a,
		const VecBase< T, Size > &	b )

inlinenodiscard

Definition at line 57 of file BLI_math_vector.hh.

References b, BLI_UNROLL_MATH_VEC_FUNC_VEC_VEC, and min().

◆ min() [3/4]

template<typename T, int Size>

VecBase< T, Size > blender::math::min ( Span< VecBase< T, Size > > values )

inlinenodiscard

Element-wise minimum of the passed vectors.

Definition at line 66 of file BLI_math_vector.hh.

References BLI_assert, min, result, and v.

◆ min() [4/4]

template<typename T, int Size>

VecBase< T, Size > blender::math::min ( std::initializer_list< VecBase< T, Size > > values )

inlinenodiscard

Element-wise minimum of the passed vectors.

Definition at line 82 of file BLI_math_vector.hh.

References min.

◆ min_inplace()

template<typename T>

void blender::math::min_inplace	(	T &	a,
		const T &	b )

inline

Definition at line 62 of file BLI_math_base.hh.

References b, and T.

Referenced by blender::io::obj::Geometry::track_vertex_index().

◆ min_max() [1/2]

template<typename T>

void blender::math::min_max	(	const T &	value,
		T &	min,
		T &	max )

inline

Definition at line 99 of file BLI_math_base.hh.

References max(), min(), and T.

◆ min_max() [2/2]

template<typename T, int Size>

void blender::math::min_max	(	const VecBase< T, Size > &	vector,
		VecBase< T, Size > &	min,
		VecBase< T, Size > &	max )

inline

Definition at line 326 of file BLI_math_vector.hh.

References max(), and min().

◆ mod() [1/3]

template<typename T>

T blender::math::mod	(	const T &	a,
		const T &	b )

inline

Definition at line 79 of file BLI_math_base.hh.

References b, and T.

Referenced by blender::deform_drawing(), blender::ed::greasepencil::get_control_point_type(), blender::get_rand_matrix(), mod(), mod(), blender::noise::perlin_signed(), blender::noise::perlin_signed(), blender::noise::perlin_signed(), blender::noise::perlin_signed(), blender::ed::greasepencil::primitive_calulate_curve_positions(), safe_mod(), and blender::geometry::sample_curve_attribute().

◆ mod() [2/3]

template<typename T, int Size>

VecBase< T, Size > blender::math::mod	(	const VecBase< T, Size > &	a,
		const T &	b )

inlinenodiscard

Definition at line 164 of file BLI_math_vector.hh.

References b, BLI_assert, i, mod(), result, and T.

◆ mod() [3/3]

template<typename T, int Size>

VecBase< T, Size > blender::math::mod	(	const VecBase< T, Size > &	a,
		const VecBase< T, Size > &	b )

inlinenodiscard

Definition at line 158 of file BLI_math_vector.hh.

References b, BLI_UNROLL_MATH_VEC_FUNC_VEC_VEC, and mod().

◆ mod_periodic()

template<typename T>

T blender::math::mod_periodic	(	const T &	a,
		const T &	b )

inline

Repeats the saw-tooth pattern even on negative numbers. ex: mod_periodic(-3, 4) = 1, mod(-3, 4)= -3. This will cause undefined behavior for negative b.

Definition at line 127 of file BLI_math_base.hh.

References abs(), b, BLI_assert, floor(), and T.

Referenced by blender::compositor::bokeh(), blender::ed::transform::curves::cyclic_curve_connected_point_distances(), blender::nodes::node_fn_bit_math_cc::get_multi_function(), blender::nodes::node_fn_integer_math_cc::get_multi_function(), blender::nodes::node_geo_mesh_topology_offset_corner_in_face_cc::OffsetCornerInFaceFieldInput::get_varray_for_context(), blender::nodes::node_geo_offset_point_in_curve_cc::ControlPointNeighborFieldInput::get_varray_for_context(), blender::tests::TEST(), blender::math::AngleFraction< T >::wrapped(), and blender::math::AngleRadianBase< float >::wrapped().

◆ normal_tri()

template<typename T>

VecBase< T, 3 > blender::math::normal_tri	(	const VecBase< T, 3 > &	v1,
		const VecBase< T, 3 > &	v2,
		const VecBase< T, 3 > &	v3 )

inlinenodiscard

Return normal vector to a triangle. The result is normalized but can still be degenerate.

Definition at line 618 of file BLI_math_vector.hh.

References cross_tri(), normalize, and v2.

Referenced by blender::ed::sculpt_paint::calc_area_normal_and_center_node_bmesh(), blender::io::stl::export_frame(), blender::bke::mesh::face_normal_calc(), from_triangle(), and blender::bke::pbvh::node_raycast_bmesh().

◆ normalize() [1/5]

template<typename T>

DualQuaternionBase< T > blender::math::normalize ( const DualQuaternionBase< T > & dual_quat )

nodiscard

Apply all accumulated weights to the dual-quaternions. Also make sure the rotation quaternions is normalized.

Note: The C version of this function does not normalize the quaternion. This makes other operations like transform and matrix conversion more complex.; Returns identity DualQuaternion if degenerate.

Definition at line 445 of file BLI_math_quaternion.hh.

References dot(), blender::math::DualQuaternionBase< T >::identity(), blender::math::DualQuaternionBase< T >::quat, blender::math::DualQuaternionBase< T >::quat_weight, blender::math::DualQuaternionBase< T >::scale, blender::math::DualQuaternionBase< T >::scale_weight, sqrt(), T, and blender::math::DualQuaternionBase< T >::trans.

◆ normalize() [2/5]

template<typename T, int NumCol, int NumRow>

MatBase< T, NumCol, NumRow > blender::math::normalize ( const MatBase< T, NumCol, NumRow > & a )

nodiscard

Normalize each column of the matrix individually.

Definition at line 778 of file BLI_math_matrix.hh.

References i, normalize(), result, and blender::unroll().

◆ normalize() [3/5]

template<typename T, int NumCol, int NumRow, int SrcNumCol, int SrcNumRow, int SrcStartCol, int SrcStartRow, int SrcAlignment>

MatBase< T, NumCol, NumRow > blender::math::normalize ( const MatView< T, NumCol, NumRow, SrcNumCol, SrcNumRow, SrcStartCol, SrcStartRow, SrcAlignment > & a )

nodiscard

Definition at line 747 of file BLI_math_matrix.hh.

References i, normalize(), result, and blender::unroll().

◆ normalize() [4/5]

template<typename T>

QuaternionBase< T > blender::math::normalize ( const QuaternionBase< T > & q )

inlinenodiscard

Return a unit quaternion representing the same rotation as q or the identity quaternion if q is ill-formed.

Definition at line 256 of file BLI_math_quaternion.hh.

References len, normalize_and_get_length(), and T.

◆ normalize() [5/5]

template<typename T, int Size>

VecBase< T, Size > blender::math::normalize ( const VecBase< T, Size > & v )

inlinenodiscard

Definition at line 537 of file BLI_math_vector.hh.

References len, normalize_and_get_length(), T, and v.

◆ normalize_and_get_length() [1/2]

template<typename T>

QuaternionBase< T > blender::math::normalize_and_get_length	(	const QuaternionBase< T > &	q,
		T &	out_length )

inlinenodiscard

Definition at line 249 of file BLI_math_quaternion.hh.

References dot(), blender::math::QuaternionBase< T >::identity(), sqrt(), and T.

Referenced by blender::math::AxisAngleBase< T, AngleT >::AxisAngleBase(), blender::ed::sculpt_paint::cloth::cloth_brush_solve_collision(), convexhull_2d_angle_iter_init(), convexhull_2d_angle_iter_step_on_axis(), distfactor_to_bone(), blender::math::QuaternionBase< T >::expmap(), blender::geometry::extend_curve_curved(), blender::ed::greasepencil::find_curve_intersections(), from_vector(), blender::ed::sculpt_paint::grease_pencil_fill_extension_cut(), blender::bke::node_foreach_working_space_color(), normalize(), normalize(), normalize_and_get_size(), normalize_and_get_size(), blender::bke::pbvh::normals_calc_verts_simple(), orthogonalize(), blender::ed::sculpt_paint::paint_line_strokes_spacing(), blender::ed::sculpt_paint::raycast_init(), blender::ed::transform::raycastMesh(), blender::geometry::curve_constraints::solve_length_and_collision_constraints(), blender::ed::transform::transform_mesh_edge_slide_data_create(), blender::bke::greasepencil::update_curve_plane_normal_cache(), blender::math::QuaternionBase< T >::wrapped_around(), and blender::write_fill_transforms().

◆ normalize_and_get_length() [2/2]

template<typename T, int Size>

VecBase< T, Size > blender::math::normalize_and_get_length	(	const VecBase< T, Size > &	v,
		T &	out_length )

inlinenodiscard

Definition at line 521 of file BLI_math_vector.hh.

References length_squared(), sqrt, T, and v.

◆ normalize_and_get_size() [1/2]

template<typename T, int NumCol, int NumRow, typename VectorT>

MatBase< T, NumCol, NumRow > blender::math::normalize_and_get_size	(	const MatBase< T, NumCol, NumRow > &	a,
		VectorT &	r_size )

nodiscard

Normalize each column of the matrix individually. Return the length of each column vector.

Definition at line 786 of file BLI_math_matrix.hh.

References BLI_STATIC_ASSERT, i, normalize_and_get_length(), result, and blender::unroll().

Referenced by blender::nodes::node_fn_separate_transform_cc::SeparateTransformFunction::call(), blender::eevee::Light::sync(), blender::tests::TEST(), to_rot_scale(), and to_rot_scale().

◆ normalize_and_get_size() [2/2]

template<typename T, int NumCol, int NumRow, int SrcNumCol, int SrcNumRow, int SrcStartCol, int SrcStartRow, int SrcAlignment, typename VectorT>

MatBase< T, NumCol, NumRow > blender::math::normalize_and_get_size	(	const MatView< T, NumCol, NumRow, SrcNumCol, SrcNumRow, SrcStartCol, SrcStartRow, SrcAlignment > &	a,
		VectorT &	r_size )

nodiscard

Definition at line 765 of file BLI_math_matrix.hh.

References BLI_STATIC_ASSERT, i, normalize_and_get_length(), result, and blender::unroll().

◆ normalized_to_quaternion_safe()

template<typename T>

QuaternionBase< T > blender::math::normalized_to_quaternion_safe ( const MatBase< T, 3, 3 > & mat )

inlinenodiscard

This is "safe" in the sense that the input matrix may not actually encode a rotation but can also contain shearing etc.

Definition at line 1285 of file BLI_math_matrix.hh.

References to_euler(), and to_quaternion().

Referenced by blender::nodes::node_fn_separate_transform_cc::SeparateTransformFunction::call(), blender::bke::float4x4_to_quaternion(), blender::bke::attribute_math::mix3(), and blender::tests::TEST().

◆ operator<<() [1/4]

std::ostream & blender::math::operator<<	(	std::ostream &	stream,
		const Axis	axis )

Definition at line 15 of file math_basis_types.cc.

◆ operator<<() [2/4]

std::ostream & blender::math::operator<<	(	std::ostream &	stream,
		const AxisSigned	axis )

Definition at line 29 of file math_basis_types.cc.

◆ operator<<() [3/4]

std::ostream & blender::math::operator<<	(	std::ostream &	stream,
		const CartesianBasis &	rot )

Definition at line 44 of file math_basis_types.cc.

◆ operator<<() [4/4]

std::ostream & blender::math::operator<<	(	std::ostream &	stream,
		EulerOrder	order )

Definition at line 142 of file math_rotation.cc.

References XYZ, XZY, YXZ, YZX, ZXY, and ZYX.

◆ operator<=() [1/2]

bool blender::math::operator<=	(	const Axis::Value	a,
		const Axis::Value	b )

constexpr

Definition at line 185 of file BLI_math_basis_types.hh.

References b.

◆ operator<=() [2/2]

bool blender::math::operator<=	(	const AxisSigned::Value	a,
		const AxisSigned::Value	b )

constexpr

Definition at line 190 of file BLI_math_basis_types.hh.

References b.

◆ orthogonal() [1/2]

template<typename T>

VecBase< T, 2 > blender::math::orthogonal ( const VecBase< T, 2 > & v )

inlinenodiscard

Calculates a perpendicular vector to v.

Note: Returned vector can be in any perpendicular direction.

Definition at line 751 of file BLI_math_vector.hh.

References v.

◆ orthogonal() [2/2]

template<typename T>

VecBase< T, 3 > blender::math::orthogonal ( const VecBase< T, 3 > & v )

inlinenodiscard

Calculates a perpendicular vector to v.

Note: Returned vector can be in any perpendicular direction.; Returned vector might not the same length as v.

Definition at line 733 of file BLI_math_vector.hh.

References dominant_axis(), and v.

Referenced by blender::math::AxisAngleBase< T, AngleT >::AxisAngleBase(), blender::ed::transform::isect_face_dst(), and blender::eevee::IrradianceBake::raylists_build().

◆ orthogonalize()

template<typename MatT>

MatT blender::math::orthogonalize	(	const MatT &	mat,
		const Axis	axis )

nodiscard

This returns a version of mat with orthonormal basis axes. This leaves the given axis untouched.

In other words this removes the shear of the matrix. However this doesn't properly account for volume preservation, and so, the axes keep their respective length.

Note: Prefer using from_up_axis to create a orthogonal basis around a vector.

The secondary axis is chosen as follow (X->Y, Y->X, Z->X). If this axis is co-planar try the third axis. If also co-planar, make up an axis by shuffling the primary axis coordinates (XYZ > YZX).

Definition at line 1528 of file BLI_math_matrix.hh.

References BLI_assert_unreachable, cross, dot(), normalize, normalize_and_get_length(), R, result, scale(), T, blender::math::Axis::X, blender::math::Axis::Y, and blender::math::Axis::Z.

Referenced by to_dual_quaternion().

◆ polar_decompose()

template<typename T>

void blender::math::polar_decompose	(	const MatBase< T, 3, 3 > &	mat3,
		MatBase< T, 3, 3 > &	r_U,
		MatBase< T, 3, 3 > &	r_P )

static

Right polar decomposition: M = UP

U is the rotation-like component, the closest orthogonal matrix to M. P is the scaling-like component, defined in U space.

See https://en.wikipedia.org/wiki/Polar_decomposition for more.

WORKAROUND: (ComputeThinU | ComputeThinV) must be set as runtime parameters in Eigen < 3.4.0. But this requires the matrix type to be dynamic to avoid an assert.

Definition at line 292 of file math_matrix.cc.

References blender::MatBase< T, NumCol, NumRow, Alignment >::base_ptr(), from_scale(), polar_decompose(), transpose, V, and W.

Referenced by interpolate(), and polar_decompose().

◆ pow() [1/4]

template<typename T>

QuaternionBase< T > blender::math::pow	(	const QuaternionBase< T > &	q,
		const T &	y )

nodiscard

Raise a unit Quaternion q to the real y exponent.

Note: This only works on unit quaternions and y != 0.; This is not a per component power.

Definition at line 202 of file BLI_math_quaternion.hh.

References BLI_assert, cos(), blender::math::QuaternionBase< T >::imaginary_part(), is_unit_scale(), normalize, safe_acos(), sin(), T, blender::math::QuaternionBase< T >::w, and y.

◆ pow() [2/4]

template<typename T>

T blender::math::pow	(	const T &	x,
		const T &	power )

inline

Definition at line 194 of file BLI_math_base.hh.

References power(), T, and x.

Referenced by blender::nodes::node_composite_glare_cc::GlareOperation::compute_fog_glow_field_of_view(), do_version_glare_node_options_to_inputs(), blender::nodes::node_composite_kuwahara_cc::ConvertKuwaharaOperation::execute_anisotropic_cpu(), blender::geometry::extend_curve_curved(), blender::nodes::node_fn_integer_math_cc::get_multi_function(), blender::nodes::node_composite_colorbalance_cc::lift_gamma_gain(), blender::nodes::node_composite_colorbalance_cc::offset_power_slope(), pow(), pow(), blender::ed::greasepencil::simplify_fixed(), blender::ed::sculpt_paint::simplify_fixed(), blender::simplify_fixed(), and blender::math::tests::TEST().

◆ pow() [3/4]

template<typename T, int Size>

VecBase< T, Size > blender::math::pow	(	const VecBase< T, Size > &	x,
		const T &	y )

inlinenodiscard

Return the value of x raised to the y power. The result is undefined if x < 0 or if x = 0 and y <= 0.

Definition at line 228 of file BLI_math_vector.hh.

References i, pow(), result, T, x, and y.

◆ pow() [4/4]

template<typename T, int Size>

VecBase< T, Size > blender::math::pow	(	const VecBase< T, Size > &	x,
		const VecBase< T, Size > &	y )

inlinenodiscard

Return the value of x raised to the y power. The result is undefined if x < 0 or if x = 0 and y <= 0.

Definition at line 272 of file BLI_math_vector.hh.

References BLI_UNROLL_MATH_VEC_FUNC_VEC_VEC, pow(), x, and y.

◆ project()

template<typename T, int Size>

VecBase< T, Size > blender::math::project	(	const VecBase< T, Size > &	p,
		const VecBase< T, Size > &	v_proj )

inlinenodiscard

Project p onto v_proj . Returns zero vector if v_proj is degenerate (zero length).

Definition at line 511 of file BLI_math_vector.hh.

References dot(), is_zero(), and UNLIKELY.

◆ project_point() [1/4]

template float2 blender::math::project_point	(	const float3x3 &	mat,
		const float2 &	point )

extern

◆ project_point() [2/4]

template float3 blender::math::project_point	(	const float4x4 &	mat,
		const float3 &	point )

extern

◆ project_point() [3/4]

template<typename T, int N, int NumRow>

VecBase< T, N > blender::math::project_point	(	const MatBase< T, N+1, NumRow > &	mat,
		const VecBase< T, N > &	point )

Definition at line 1665 of file BLI_math_matrix.hh.

References abs(), N, and T.

◆ project_point() [4/4]

template<typename MatT, typename VectorT>

VectorT blender::math::project_point	(	const MatT &	mat,
		const VectorT &	point )

nodiscard

Project a point using a matrix (location & rotation & scale & perspective divide).

Referenced by blender::ed::sculpt_paint::do_brush_action(), blender::nodes::node_fn_project_point_cc::node_build_multi_function(), blender::ed::transform::EdgeSlideData::project(), blender::ed::transform::VertSlideData::project(), blender::io::grease_pencil::GreasePencilExporter::project_to_screen(), blender::eevee::ShadowModule::screen_pixel_radius(), blender::tests::TEST(), blender::ed::transform::VertSlideData::update_active_edges(), and blender::eevee::VolumeObjectBounds::VolumeObjectBounds().

◆ pseudo_invert() [1/7]

template double2x2 blender::math::pseudo_invert	(	const double2x2 &	mat,
		double	epsilon )

References pseudo_invert().

◆ pseudo_invert() [2/7]

template double3x3 blender::math::pseudo_invert	(	const double3x3 &	mat,
		double	epsilon )

References pseudo_invert().

◆ pseudo_invert() [3/7]

template double4x4 blender::math::pseudo_invert	(	const double4x4 &	mat,
		double	epsilon )

References pseudo_invert().

◆ pseudo_invert() [4/7]

template float2x2 blender::math::pseudo_invert	(	const float2x2 &	mat,
		float	epsilon )

References pseudo_invert().

◆ pseudo_invert() [5/7]

template float3x3 blender::math::pseudo_invert	(	const float3x3 &	mat,
		float	epsilon )

References pseudo_invert().

◆ pseudo_invert() [6/7]

template float4x4 blender::math::pseudo_invert	(	const float4x4 &	mat,
		float	epsilon )

References pseudo_invert().

◆ pseudo_invert() [7/7]

template<typename T, int Size>

MatBase< T, Size, Size > blender::math::pseudo_invert	(	const MatBase< T, Size, Size > &	mat,
		T	epsilon = 1e-8 )

nodiscard

Compute Moore-Penrose pseudo inverse of matrix. Singular values below epsilon are ignored for stability (truncated SVD). Gives a good enough approximation of the regular inverse matrix if the given matrix is non-invertible (ex: degenerate transform). The returned pseudo inverse matrix A+ of input matrix A will not satisfy A+ * A = Identity but will satisfy A * A+ * A = A. For more detail, see https://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_inverse.

Compute the Single Value Decomposition of an arbitrary matrix A That is compute the 3 matrices U,W,V with U column orthogonal (m,n) ,W a diagonal matrix and V an orthogonal square matrix s.t.A = U.W.Vt. From this decomposition it is trivial to compute the (pseudo-inverse) of A as Ainv = V.Winv.transpose(U).

WORKAROUND: (ComputeThinU | ComputeThinV) must be set as runtime parameters in Eigen < 3.4.0. But this requires the matrix type to be dynamic to avoid an assert.

Definition at line 223 of file math_matrix.cc.

References blender::MatBase< T, NumCol, NumRow, Alignment >::base_ptr(), from_scale(), i, invert(), pseudo_invert(), T, transpose, U, blender::unroll(), V, and W.

Referenced by blender::ed::transform::pointcloud::createTransPointCloudVerts(), blender::ed::transform::curves::curve_populate_trans_data_structs(), pseudo_invert(), pseudo_invert(), pseudo_invert(), pseudo_invert(), pseudo_invert(), pseudo_invert(), pseudo_invert(), and blender::tests::TEST().

◆ rcp() [1/2]

template<typename T>

T blender::math::rcp ( const T & a )

inline

Definition at line 160 of file BLI_math_base.hh.

References T.

◆ rcp() [2/2]

template<typename T, int Size>

VecBase< T, Size > blender::math::rcp ( const VecBase< T, Size > & a )

inlinenodiscard

Per-element inverse. Zero elements are evaluated to NaN.

Definition at line 397 of file BLI_math_vector.hh.

References BLI_UNROLL_MATH_VEC_OP_VEC, and rcp().

◆ reduce_add()

template<typename T, int Size>

T blender::math::reduce_add ( const VecBase< T, Size > & a )

inlinenodiscard

Returns: the sum of the components of a vector.

Definition at line 699 of file BLI_math_vector.hh.

References i, result, and T.

Referenced by average(), blender::compositor::compute_boundary_coefficient(), blender::compositor::compute_boundary_coefficient(), blender::compositor::compute_feedforward_coefficient(), blender::compositor::compute_normalization_scale(), blender::nodes::node_composite_glare_cc::GlareOperation::karis_brightness_weighted_sum(), and blender::draw::overlay::Resources::update_theme_settings().

◆ reduce_max()

template<typename T, int Size>

T blender::math::reduce_max ( const VecBase< T, Size > & a )

inlinenodiscard

Returns: the maximum component of a vector.

Definition at line 671 of file BLI_math_vector.hh.

References i, result, and T.

Referenced by blender::ed::sculpt_paint::calc_brush_cube_distances(), blender::nodes::node_composite_relative_to_pixel_cc::RelativeToPixelOperation::compute_reference_size(), blender::compositor::deriche_gaussian_blur(), do_version_glare_node_options_to_inputs(), blender::ed::vse::draw_histogram(), evaluate_film_like(), blender::nodes::node_composite_glare_cc::GlareOperation::execute_fog_glow(), blender::ed::greasepencil::fit_strokes_to_view(), blender::io::obj::geometry_to_blender_objects(), blender::eevee::IrradianceBake::init(), blender::eevee::VolumeModule::init(), blender::nodes::node_composite_glare_cc::GlareOperation::karis_brightness_weighted_sum(), blender::draw::overlay::Bounds::object_sync(), blender::draw::overlay::LightProbes::object_sync(), blender::eevee::Film::overscan_pixels_get(), blender::compositor::recursive_gaussian_blur(), blender::eevee::VolumePipeline::register_and_get_layer(), blender::ed::sculpt_paint::dyntopo::sculpt_detail_flood_fill_exec(), blender::compositor::van_vliet_gaussian_blur(), and blender::ed::vse::view_frame_preview_scope().

◆ reduce_min()

template<typename T, int Size>

T blender::math::reduce_min ( const VecBase< T, Size > & a )

inlinenodiscard

Returns: the minimum component of a vector.

Definition at line 685 of file BLI_math_vector.hh.

References i, result, and T.

Referenced by blender::nodes::node_composite_glare_cc::GlareOperation::compute_bloom_chain_length(), blender::nodes::node_composite_relative_to_pixel_cc::RelativeToPixelOperation::compute_reference_size(), do_version_glare_node_bloom_strength(), evaluate_film_like(), and blender::eevee::IrradianceBake::surfels_create().

◆ reduce_mul()

template<typename T, int Size>

T blender::math::reduce_mul ( const VecBase< T, Size > & a )

inlinenodiscard

Returns: the product of the components of a vector.

Definition at line 711 of file BLI_math_vector.hh.

References i, result, and T.

Referenced by blender::eevee::VolumeProbeModule::init(), and blender::draw::overlay::Fluids::object_sync().

◆ reflect()

template<typename T, int Size>

VecBase< T, Size > blender::math::reflect	(	const VecBase< T, Size > &	incident,
		const VecBase< T, Size > &	normal )

inlinenodiscard

Definition at line 486 of file BLI_math_vector.hh.

References BLI_assert, dot(), and is_unit_scale().

◆ refract()

template<typename T, int Size>

VecBase< T, Size > blender::math::refract	(	const VecBase< T, Size > &	incident,
		const VecBase< T, Size > &	normal,
		const T &	eta )

inlinenodiscard

Definition at line 494 of file BLI_math_vector.hh.

References dot(), sqrt, and T.

◆ rotate() [1/6]

template<typename T, typename RotT, typename AngleT>

AxisAngleBase< T, AngleT > blender::math::rotate	(	const AxisAngleBase< T, AngleT > &	a,
		const RotT &	b )

nodiscard

Rotate a by b. In other word, insert the b rotation before a.

Note: Since a is an AxisAngle it will cast both a and b to Quaternion. This might introduce some precision loss and have performance implication.

Definition at line 199 of file BLI_math_rotation.hh.

References b.

◆ rotate() [2/6]

template<typename T, typename RotT>

Euler3Base< T > blender::math::rotate	(	const Euler3Base< T > &	a,
		const RotT &	b )

nodiscard

Rotate a by b. In other word, insert the b rotation before a.

Note: Since a is an Euler3 it will cast both a and b to MatBase<T, 3, 3>. This might introduce some precision loss and have performance implication.

Definition at line 212 of file BLI_math_rotation.hh.

References b, from_rotation(), blender::math::Euler3Base< T >::order(), and to_euler().

◆ rotate() [3/6]

template<typename T, typename RotT>

EulerXYZBase< T > blender::math::rotate	(	const EulerXYZBase< T > &	a,
		const RotT &	b )

nodiscard

Rotate a by b. In other word, insert the b rotation before a.

Note: Since a is an EulerXYZ it will cast both a and b to MatBase<T, 3, 3>. This might introduce some precision loss and have performance implication.

Definition at line 205 of file BLI_math_rotation.hh.

References b, from_rotation(), and to_euler().

◆ rotate() [4/6]

template<typename T, int NumCol, int NumRow, typename AngleT>

MatBase< T, NumCol, NumRow > blender::math::rotate	(	const MatBase< T, NumCol, NumRow > &	mat,
		const AxisAngleBase< T, AngleT > &	rotation )

nodiscard

Definition at line 682 of file BLI_math_matrix.hh.

References blender::math::AxisAngleBase< T, AngleT >::angle(), blender::math::AxisAngleBase< T, AngleT >::axis(), cos, from_rotation(), result, sin, T, and blender::unroll().

◆ rotate() [5/6]

template<typename T, int NumCol, int NumRow, typename RotationT>

MatBase< T, NumCol, NumRow > blender::math::rotate	(	const MatBase< T, NumCol, NumRow > &	mat,
		const RotationT &	rotation )

nodiscard

Equivalent to mat * from_rotation(rotation) but with fewer operation. Optimized for AxisAngle rotation on basis vector (i.e: AxisAngle({1, 0, 0}, 0.2)).

References b, e, scale(), T, and transform().

Referenced by blender::eevee::LookdevWorld::LookdevWorld(), and blender::tests::TEST().

◆ rotate() [6/6]

template<typename T, typename RotT>

QuaternionBase< T > blender::math::rotate	(	const QuaternionBase< T > &	a,
		const RotT &	b )

nodiscard

Rotate a by b. In other word, insert the b rotation before a.

Note: Since a is a Quaternion it will cast b to a Quaternion. This might introduce some precision loss and have performance implication.

Definition at line 193 of file BLI_math_rotation.hh.

References b.

◆ rotate_around_axis()

float3 blender::math::rotate_around_axis	(	const float3 &	vector,
		const float3 &	center,
		const float3 &	axis,
		float	angle )

Rotate any arbitrary vector around the center position, with a unit-length axis and the specified angle.

Definition at line 129 of file math_rotation.cc.

References angle(), axis_angle_normalized_to_mat3(), mul_m3_v3(), and result.

Referenced by blender::ed::sculpt_paint::boundary::calc_twist_position().

◆ rotate_direction_around_axis()

float3 blender::math::rotate_direction_around_axis	(	const float3 &	direction,
		const float3 &	axis,
		float	angle )

Rotate the unit-length direction around the unit-length axis by the angle.

Definition at line 112 of file math_rotation.cc.

References angle(), BLI_assert, cross(), diff(), dot(), is_unit(), is_zero(), and UNLIKELY.

Referenced by blender::bke::curves::poly::calculate_next_normal(), blender::bke::curves::poly::calculate_normals_minimum(), blender::bke::rotate_directions_around_axes(), blender::math::tests::TEST(), and blender::ed::sculpt_paint::tilt_apply_to_normal().

◆ rotation_between() [1/3]

CartesianBasis blender::math::rotation_between	(	const AxisSigned	a_forward,
		const AxisSigned	b_forward )

inlinenodiscard

Create an CartesianBasis for converting from an a orientation defined only by its forward vector to a b orientation defined only by its forward vector. Rotation is given to be non flipped and deterministic.

Definition at line 430 of file BLI_math_basis_types.hh.

References abs, from_orthonormal_axes(), blender::math::AxisSigned::next_after(), rotation_between(), and sign().

◆ rotation_between() [2/3]

CartesianBasis blender::math::rotation_between	(	const CartesianBasis &	a,
		const CartesianBasis &	b )

inlinenodiscard

Create an CartesianBasis for converting from a orientation to b orientation.

Definition at line 415 of file BLI_math_basis_types.hh.

References abs, blender::math::CartesianBasis::axes, b, sign(), blender::math::CartesianBasis::x(), blender::math::CartesianBasis::y(), and blender::math::CartesianBasis::z().

Referenced by angle_between(), angle_between_signed(), from_tracking(), rotation_between(), blender::math::tests::TEST(), blender::math::tests::TEST(), blender::math::tests::TEST(), and blender::math::tests::TEST().

◆ rotation_between() [3/3]

template<typename T>

QuaternionBase< T > blender::math::rotation_between	(	const QuaternionBase< T > &	a,
		const QuaternionBase< T > &	b )

nodiscard

Return rotation from orientation a to orientation b into another quaternion.

Definition at line 220 of file BLI_math_rotation.hh.

References b, and invert().

◆ round() [1/2]

template<typename T>

T blender::math::round ( const T & a )

inline

Definition at line 117 of file BLI_math_base.hh.

References T.

Referenced by blender::seq::apply_text_alignment(), blender::geometry::assign_samples_to_segments(), blender::ed::sculpt_paint::greasepencil::brush_point_influence_mask(), blender::ed::sculpt_paint::greasepencil::EraseOperationExecutor::compute_piecewise_linear_falloff(), blender::bke::attribute_math::DefaultMixerStruct< int2 >::double_to_int(), blender::seq::final_image_cache_get(), blender::seq::final_image_cache_put(), blender::bke::attribute_math::DefaultMixerStruct< short2 >::float_to_int(), blender::get_build_factor(), blender::ed::sculpt_paint::greasepencil::GreasePencilStrokeOperationCommon::init_auto_masking(), blender::ed::sculpt_paint::greasepencil::EraseOperationExecutor::intersections_segment_circle_integers(), blender::ed::space_node::mark_sockets_collapsed_recursive(), blender::ed::transform::node_snap_grid_apply(), blender::ed::space_node::node_update_basis(), blender::ed::space_node::node_update_basis_buttons(), blender::ed::space_node::node_update_basis_from_declaration(), blender::ed::space_node::node_update_collapsed(), round(), blender::compositor::SMAAArea(), blender::compositor::SMAABlendingWeightCalculationPS(), blender::compositor::SMAADecodeDiagBilinearAccess(), blender::compositor::SMAADecodeDiagBilinearAccess(), blender::ed::transform::snap_grid(), blender::seq::source_image_cache_get(), blender::seq::source_image_cache_put(), store_pixel(), blender::seq::thumbnail_cache_get(), and uv_copy_mirrored_faces().

◆ round() [2/2]

template<typename T, int Size>

VecBase< T, Size > blender::math::round ( const VecBase< T, Size > & a )

inlinenodiscard

Definition at line 358 of file BLI_math_vector.hh.

References BLI_UNROLL_MATH_VEC_OP_VEC, and round().

◆ safe_acos()

template<typename T>

T blender::math::safe_acos ( const T & a )

inline

Definition at line 224 of file BLI_math_base.hh.

References acos(), blender::math::numbers::pi, T, and UNLIKELY.

Referenced by angle_between(), angle_of(), angle_of_signed(), from_triangle(), from_vector(), blender::ed::sculpt_paint::auto_mask::normal_calc(), pow(), and to_quaternion_legacy().

◆ safe_acos_approx()

float blender::math::safe_acos_approx ( float x )

inline

Faster/approximate version of safe_acos. Max error 4.51803e-5 (0.00258 degrees).

Definition at line 236 of file BLI_math_base.hh.

References float, blender::math::numbers::pi, and x.

Referenced by blender::bke::mesh::accumulate_fan_normal(), accumulate_vertex_normals_poly_v3(), accumulate_vertex_normals_tri_v3(), accumulate_vertex_normals_v3(), bm_loop_normal_accum(), bm_mesh_loops_calc_normals_for_loop(), bm_vert_calc_normals_accum_loop(), calc_tangent_spaces(), blender::bke::mesh::corner_fan_space_define(), and blender::bke::mesh::corner_space_custom_normal_to_data().

◆ safe_divide() [1/3]

template<typename T>

T blender::math::safe_divide	(	const T &	a,
		const T &	b )

inline

Definition at line 107 of file BLI_math_base.hh.

References b, and T.

◆ safe_divide() [2/3]

template<typename T, int Size>

VecBase< T, Size > blender::math::safe_divide	(	const VecBase< T, Size > &	a,
		const T &	b )

inlinenodiscard

Returns 0 if denominator is exactly equal to 0.

Definition at line 346 of file BLI_math_vector.hh.

References b, and T.

◆ safe_divide() [3/3]

template<typename T, int Size>

VecBase< T, Size > blender::math::safe_divide	(	const VecBase< T, Size > &	a,
		const VecBase< T, Size > &	b )

inlinenodiscard

Returns 0 if denominator is exactly equal to 0.

Definition at line 336 of file BLI_math_vector.hh.

References b, BLI_UNROLL_MATH_VEC_FUNC_VEC_VEC, and safe_divide().

◆ safe_floored_mod()

template<typename T>

T blender::math::safe_floored_mod	(	const T &	a,
		const T &	b )

inline

Definition at line 94 of file BLI_math_base.hh.

References b, and T.

◆ safe_mod() [1/3]

template<typename T>

T blender::math::safe_mod	(	const T &	a,
		const T &	b )

inline

Definition at line 84 of file BLI_math_base.hh.

References b, and T.

Referenced by safe_mod().

◆ safe_mod() [2/3]

template<typename T, int Size>

VecBase< T, Size > blender::math::safe_mod	(	const VecBase< T, Size > &	a,
		const T &	b )

inlinenodiscard

Safe version of mod(a, b) that returns 0 if b is equal to 0.

Definition at line 188 of file BLI_math_vector.hh.

References b, i, mod(), result, and T.

◆ safe_mod() [3/3]

template<typename T, int Size>

VecBase< T, Size > blender::math::safe_mod	(	const VecBase< T, Size > &	a,
		const VecBase< T, Size > &	b )

inlinenodiscard

Safe version of mod(a, b) that returns 0 if b is equal to 0.

Definition at line 178 of file BLI_math_vector.hh.

References b, BLI_UNROLL_MATH_VEC_FUNC_VEC_VEC, and safe_mod().

◆ safe_pow() [1/2]

template<typename T>

T blender::math::safe_pow	(	const T &	x,
		const T &	power )

inline

Definition at line 199 of file BLI_math_base.hh.

References power(), T, and x.

Referenced by blender::nodes::node_shader_gamma_cc::node_build_multi_function(), and safe_pow().

◆ safe_pow() [2/2]

template<typename T, int Size>

VecBase< T, Size > blender::math::safe_pow	(	const VecBase< T, Size > &	x,
		const T &	y )

inlinenodiscard

Return the value of x raised to the y power. The result is x if x < 0 or if x = 0 and y <= 0.

Definition at line 242 of file BLI_math_vector.hh.

References i, result, safe_pow(), T, x, and y.

◆ safe_rcp() [1/2]

template<typename T>

T blender::math::safe_rcp ( const T & a )

inline

Definition at line 168 of file BLI_math_base.hh.

References T.

◆ safe_rcp() [2/2]

template<typename T, int Size>

VecBase< T, Size > blender::math::safe_rcp ( const VecBase< T, Size > & a )

inlinenodiscard

Per-element inverse. Zero elements are evaluated to zero.

Definition at line 407 of file BLI_math_vector.hh.

References BLI_UNROLL_MATH_VEC_OP_VEC, and safe_rcp().

◆ safe_sqrt()

template<typename T, int Size>

VecBase< T, Size > blender::math::safe_sqrt ( const VecBase< T, Size > & a )

inlinenodiscard

Per-element square root. Negative elements are evaluated to zero.

Definition at line 384 of file BLI_math_vector.hh.

References i, result, and T.

Referenced by blender::tests::TEST().

◆ scale()

template<typename T, int NumCol, int NumRow, typename VectorT>

MatBase< T, NumCol, NumRow > blender::math::scale	(	const MatBase< T, NumCol, NumRow > &	mat,
		const VectorT &	scale )

nodiscard

Equivalent to mat * from_scale(scale) but with fewer operation.

Definition at line 719 of file BLI_math_matrix.hh.

References BLI_STATIC_ASSERT, result, scale(), and blender::unroll().

Referenced by blender::draw::overlay::Cursor::begin_sync(), blender::meshintersect::cdt_draw(), draw_bone_degrees_of_freedom(), blender::draw::drw_volume_object_mesh_init(), blender::bke::fill_mesh_positions(), from_loc_rot_scale(), from_loc_scale(), from_rot_scale(), from_scale(), get_dupliface_transform_from_coords(), blender::draw::gpencil::gpencil_uv_transform_get(), blender::meshintersect::graph_draw(), interpolate_fast(), interpolate_fast(), make_duplis_particle_system(), blender::draw::overlay::Bounds::object_sync(), orthogonalize(), blender::eevee::Film::pixel_jitter_get(), blender::io::grease_pencil::SVGImporter::read(), rotate(), scale(), blender::draw::overlay::ShapeCache::ShapeCache(), blender::draw::statvis_calc_thickness(), blender::eevee::IrradianceBake::surfel_raster_views_sync(), blender::eevee::Light::sync(), blender::eevee::LookdevModule::sync(), blender::tests::TEST(), blender::tests::TEST(), blender::tests::TEST(), blender::tests::TEST(), to_dual_quaternion(), and blender::write_fill_transforms().

◆ sign() [1/3]

int blender::math::sign ( const AxisSigned & axis )

inlinenodiscard

Definition at line 206 of file BLI_math_basis_types.hh.

References blender::math::AxisSigned::sign().

◆ sign() [2/3]

template<typename T>

T blender::math::sign ( const T & a )

inline

Definition at line 38 of file BLI_math_base.hh.

References T.

Referenced by blender::noise::compute_3d_orientation(), blender::nodes::node_composite_vec_blur_cc::compute_motion_rect(), float_to_half(), from_up_axis(), blender::nodes::node_fn_integer_math_cc::get_multi_function(), midpoint(), rotation_between(), rotation_between(), blender::nodes::node_fn_integer_math_cc::safe_divide_round_i(), blender::bke::greasepencil::Drawing::set_texture_matrices(), sign(), and blender::tests::TEST().

◆ sign() [3/3]

template<typename T, int Size>

VecBase< T, Size > blender::math::sign ( const VecBase< T, Size > & a )

inlinenodiscard

Returns -1 if a is less than 0, 0 if a is equal to 0, and +1 if a is greater than 0.

Definition at line 51 of file BLI_math_vector.hh.

References BLI_UNROLL_MATH_VEC_OP_VEC, and sign().

◆ sin() [1/4]

template<typename T>

T blender::math::sin ( const AngleCartesianBase< T > & a )

Definition at line 701 of file BLI_math_angle_types.hh.

References blender::math::AngleCartesianBase< T >::sin(), and T.

◆ sin() [2/4]

template<typename T>

T blender::math::sin ( const AngleFraction< T > & a )

Definition at line 714 of file BLI_math_angle_types.hh.

References sin, and T.

◆ sin() [3/4]

template<typename T>

T blender::math::sin ( const AngleRadianBase< T > & a )

Definition at line 688 of file BLI_math_angle_types.hh.

References blender::math::AngleRadianBase< T >::radian(), sin, and T.

◆ sin() [4/4]

template<typename T>

T blender::math::sin ( const T & a )

inline

Definition at line 179 of file BLI_math_base.hh.

References T.

◆ skip_transform()

bool blender::math::skip_transform ( const float4x4 & transform )

static

Definition at line 599 of file math_matrix.cc.

References blender::MatBase< float, 4, 4 >::identity(), is_equal(), skip_transform(), and transform().

Referenced by skip_transform(), transform_points(), and transform_points().

◆ sqrt() [1/2]

template<typename T>

T blender::math::sqrt ( const T & a )

inline

Definition at line 153 of file BLI_math_base.hh.

References T.

Referenced by blender::ed::sculpt_paint::greasepencil::brush_point_influence_mask(), blender::calc_min_radius_v3v3(), blender::noise::compute_2d_gabor_standard_deviation(), blender::noise::compute_3d_gabor_standard_deviation(), blender::nodes::node_composite_lensdist_cc::compute_chromatic_distortion_scale(), blender::nodes::node_composite_lensdist_cc::compute_distortion_scale(), blender::nodes::node_composite_lensdist_cc::compute_number_of_integration_steps_heuristic(), blender::nodes::node_composite_kuwahara_cc::ConvertKuwaharaOperation::execute_anisotropic_cpu(), blender::nodes::node_composite_despeckle_cc::DespeckleOperation::execute_cpu(), blender::nodes::node_composite_filter_cc::FilterOperation::execute_cpu(), blender::nodes::node_composite_dilate_cc::DilateErodeOperation::execute_distance_threshold_cpu(), blender::math::AngleCartesianBase< float >::from_point(), blender::hook_falloff(), blender::ed::sculpt_paint::greasepencil::EraseOperationExecutor::intersections_segment_circle_integers(), length(), normalize(), normalize_and_get_length(), blender::math::detail::normalized_to_quat_fast(), blender::math::AngleCartesianBase< float >::operator/, blender::compositor::SMAABlendingWeightCalculationPS(), blender::compositor::SMAANeighborhoodBlendingPS(), blender::ed::transform::snap_object_project_view3d_ex(), sqrt(), and blender::tests::TEST().

◆ sqrt() [2/2]

template<typename T, int Size>

VecBase< T, Size > blender::math::sqrt ( const VecBase< T, Size > & a )

inlinenodiscard

Per-element square root. Negative elements are evaluated to NaN.

Definition at line 374 of file BLI_math_vector.hh.

References BLI_UNROLL_MATH_VEC_OP_VEC, and sqrt().

◆ square() [1/2]

template<typename T>

T blender::math::square ( const T & a )

inline

Definition at line 209 of file BLI_math_base.hh.

References T.

Referenced by BKE_light_area(), BKE_mball_polygonize(), bmesh_find_doubles_by_distance_connected_impl(), bone_envelope_falloff(), blender::ed::sculpt_paint::cloth::brush_affected_nodes_gather(), blender::ed::sculpt_paint::filter::cache_init(), blender::ed::sculpt_paint::brushes::clay_strips::calc_node_mask(), blender::compositor::compute_fog_glow_kernel_value(), blender::compositor::compute_scaled_poles_variance_derivative(), ed_tracking_pick_plane_track(), ed_tracking_pick_point_track(), blender::nodes::node_composite_kuwahara_cc::ConvertKuwaharaOperation::execute_anisotropic_cpu(), blender::nodes::node_composite_glare_cc::GlareOperation::execute_sun_beams_cpu(), blender::compositor::find_scale_factor(), from_up_axis(), blender::compositor::morphological_distance_cpu(), blender::ed::sculpt_paint::pbvh_gather_generic(), square(), blender::tests::TEST(), to_dual_quaternion(), and uv_remove_doubles_to_selected_shared_vertex().

◆ square() [2/2]

template<typename T, int Size>

VecBase< T, Size > blender::math::square ( const VecBase< T, Size > & a )

inlinenodiscard

Per-element square.

Definition at line 279 of file BLI_math_vector.hh.

References BLI_UNROLL_MATH_VEC_OP_VEC, and square().

◆ step() [1/3]

template<typename T>

T blender::math::step	(	const T &	edge,
		const T &	value )

inline

Definition at line 74 of file BLI_math_base.hh.

References T.

Referenced by blender::draw::overlay::append_line_loop(), blender::compositor::SMAACalculateDiagWeights(), blender::compositor::SMAADetectHorizontalCornerPattern(), blender::compositor::SMAADetectVerticalCornerPattern(), blender::compositor::SMAALumaEdgeDetectionPS(), step(), step(), blender::eevee::VelocityModule::step_sync(), blender::tests::TEST(), blender::tests::TEST(), and blender::tests::TEST().

◆ step() [2/3]

template<typename T, int Size>

VecBase< T, Size > blender::math::step	(	const T &	edge,
		const VecBase< T, Size > &	value )

inlinenodiscard

Definition at line 148 of file BLI_math_vector.hh.

References i, result, step(), and T.

◆ step() [3/3]

template<typename T, int Size>

VecBase< T, Size > blender::math::step	(	const VecBase< T, Size > &	edge,
		const VecBase< T, Size > &	value )

inlinenodiscard

Definition at line 141 of file BLI_math_vector.hh.

References BLI_UNROLL_MATH_VEC_FUNC_VEC_VEC, and step().

◆ tan() [1/4]

template<typename T>

T blender::math::tan ( const AngleCartesianBase< T > & a )

Definition at line 705 of file BLI_math_angle_types.hh.

References T, and blender::math::AngleCartesianBase< T >::tan().

◆ tan() [2/4]

template<typename T>

T blender::math::tan ( const AngleFraction< T > & a )

Definition at line 718 of file BLI_math_angle_types.hh.

References T, and tan.

◆ tan() [3/4]

template<typename T>

T blender::math::tan ( const AngleRadianBase< T > & a )

Definition at line 692 of file BLI_math_angle_types.hh.

References blender::math::AngleRadianBase< T >::radian(), T, and tan.

Referenced by blender::nodes::node_composite_chroma_matte_cc::chroma_matte(), blender::draw::curve_create_edit_curves_nor(), and blender::math::projection::perspective_fov().

◆ tan() [4/4]

template<typename T>

T blender::math::tan ( const T & a )

inline

Definition at line 184 of file BLI_math_base.hh.

References T.

◆ to_angle()

template<typename T>

AngleRadianBase< T > blender::math::to_angle ( const MatBase< T, 2, 2 > & mat )

inlinenodiscard

Extract euler rotation from transform matrix.

Returns: the rotation with the smallest values from the potential candidates.

Definition at line 1184 of file BLI_math_matrix.hh.

References blender::math::detail::normalized_to_angle().

Referenced by blender::math::detail::to_rotation().

◆ to_axis_angle() [1/6]

template AxisAngle blender::math::to_axis_angle ( const Euler3 & )

extern

◆ to_axis_angle() [2/6]

template<typename T, typename AngleT = AngleRadian>

AxisAngleBase< T, AngleT > blender::math::to_axis_angle ( const Euler3Base< T > & euler )

Definition at line 106 of file BLI_math_euler.hh.

References to_axis_angle(), and to_quaternion().

◆ to_axis_angle() [3/6]

template AxisAngle blender::math::to_axis_angle ( const EulerXYZ & )

extern

◆ to_axis_angle() [4/6]

template<typename T, typename AngleT = AngleRadian>

AxisAngleBase< T, AngleT > blender::math::to_axis_angle ( const EulerXYZBase< T > & euler )

Definition at line 99 of file BLI_math_euler.hh.

References to_axis_angle(), and to_quaternion().

Referenced by blender::nodes::node_fn_rotation_to_axis_angle_cc::QuaterniontoAxisAngleFunction::call(), blender::io::fbx::create_transform_curve_data(), blender::math::QuaternionBase< T >::expmap(), blender::nodes::node_fn_axis_angle_to_rotation_cc::node_eval_inverse(), blender::math::tests::TEST(), blender::tests::TEST(), blender::tests::TEST(), blender::tests::TEST(), to_axis_angle(), to_axis_angle(), and to_axis_angle().

◆ to_axis_angle() [5/6]

template AxisAngle blender::math::to_axis_angle ( const Quaternion & )

extern

◆ to_axis_angle() [6/6]

template<typename T, typename AngleT = AngleRadian>

AxisAngleBase< T, AngleT > blender::math::to_axis_angle ( const QuaternionBase< T > & quat )

Definition at line 624 of file BLI_math_quaternion.hh.

References abs, angle(), BLI_assert, blender::math::AxisAngleBase< T, AngleT >::identity(), is_unit_scale(), length(), sign(), T, to_axis_angle(), blender::math::QuaternionBase< T >::w, blender::math::QuaternionBase< T >::x, blender::math::QuaternionBase< T >::y, and blender::math::QuaternionBase< T >::z.

◆ to_dual_quaternion()

template<typename T>

DualQuaternionBase< T > blender::math::to_dual_quaternion	(	const MatBase< T, 4, 4 > &	mat,
		const MatBase< T, 4, 4 > &	basemat )

nodiscard

Convert transformation mat with parent transform basemat into a dual-quaternion representation.

This allows volume preserving deformation for skinning.

Conversion routines between (regular quaternion, translation) and dual quaternion.

Version 1.0.0, February 7th, 2007

Changes for Blender:

renaming, style changes and optimizations
added support for scaling

Definition at line 548 of file BLI_math_quaternion.hh.

References from_rotation(), invert(), is_negative(), is_orthonormal(), length_squared(), normalize, orthogonalize(), R, scale(), square(), T, to_quaternion(), to_scale(), blender::math::QuaternionBase< T >::w, blender::math::QuaternionBase< T >::x, blender::math::Axis::Y, blender::math::QuaternionBase< T >::y, and blender::math::QuaternionBase< T >::z.

Referenced by blender::math::tests::TEST().

◆ to_euler() [1/14]

template EulerXYZ blender::math::to_euler ( const AxisAngle & )

extern

◆ to_euler() [2/14]

template Euler3 blender::math::to_euler	(	const AxisAngle &	,
		EulerOrder	)

extern

◆ to_euler() [3/14]

template<typename T, typename AngleT>

EulerXYZBase< T > blender::math::to_euler ( const AxisAngleBase< T, AngleT > & axis_angle )

Definition at line 97 of file BLI_math_axis_angle.hh.

References blender::math::AxisAngleBase< T, AngleT >::angle(), blender::math::AxisAngleBase< T, AngleT >::axis(), T, to_euler(), and to_quaternion().

◆ to_euler() [4/14]

template<typename T, typename AngleT>

Euler3Base< T > blender::math::to_euler	(	const AxisAngleBase< T, AngleT > &	axis_angle,
		EulerOrder	order )

Definition at line 90 of file BLI_math_axis_angle.hh.

References to_euler(), and to_quaternion().

Referenced by blender::io::fbx::create_transform_curve_data(), blender::io::usd::USDPointInstancerWriter::do_write(), blender::nodes::node_fn_rotation_to_euler_cc::node_build_multi_function(), blender::nodes::node_fn_euler_to_rotation_cc::node_eval_inverse(), normalized_to_quaternion_safe(), blender::bke::quaternion_to_float3(), rotate(), rotate(), blender::nodes::node_geo_rotate_instances_cc::rotate_instances(), blender::nodes::inverse_eval::set_modifier_value(), blender::nodes::inverse_eval::set_socket_value(), blender::nodes::inverse_eval::set_value_node_value(), blender::tests::TEST(), blender::tests::TEST(), blender::tests::TEST(), to_euler(), to_euler(), to_euler(), to_euler(), to_euler(), to_euler(), to_nearest_euler(), to_nearest_euler(), blender::math::detail::to_rotation(), and blender::math::detail::to_rotation().

◆ to_euler() [5/14]

template EulerXYZ blender::math::to_euler ( const AxisAngleCartesian & )

extern

◆ to_euler() [6/14]

template Euler3 blender::math::to_euler	(	const AxisAngleCartesian &	,
		EulerOrder	)

extern

◆ to_euler() [7/14]

template<typename T>

EulerXYZBase< T > blender::math::to_euler ( const MatBase< T, 3, 3 > & mat )

inlinenodiscard

Definition at line 1199 of file BLI_math_matrix.hh.

References length_manhattan(), and blender::math::detail::normalized_to_eul2().

◆ to_euler() [8/14]

template<typename T>

Euler3Base< T > blender::math::to_euler	(	const MatBase< T, 3, 3 > &	mat,
		EulerOrder	order )

inlinenodiscard

Definition at line 1190 of file BLI_math_matrix.hh.

References length_manhattan(), and blender::math::detail::normalized_to_eul2().

◆ to_euler() [9/14]

template<typename T>

EulerXYZBase< T > blender::math::to_euler ( const MatBase< T, 4, 4 > & mat )

inlinenodiscard

Definition at line 1215 of file BLI_math_matrix.hh.

References to_euler().

◆ to_euler() [10/14]

template<typename T>

Euler3Base< T > blender::math::to_euler	(	const MatBase< T, 4, 4 > &	mat,
		EulerOrder	order )

inlinenodiscard

Definition at line 1209 of file BLI_math_matrix.hh.

References to_euler().

◆ to_euler() [11/14]

template EulerXYZ blender::math::to_euler ( const Quaternion & )

extern

◆ to_euler() [12/14]

template Euler3 blender::math::to_euler	(	const Quaternion &	,
		EulerOrder	)

extern

◆ to_euler() [13/14]

template<typename T>

EulerXYZBase< T > blender::math::to_euler ( const QuaternionBase< T > & quat )

Definition at line 654 of file BLI_math_quaternion.hh.

References BLI_assert, from_rotation(), is_unit_scale(), and to_euler().

◆ to_euler() [14/14]

template<typename T>

Euler3Base< T > blender::math::to_euler	(	const QuaternionBase< T > &	quat,
		EulerOrder	order )

Definition at line 662 of file BLI_math_quaternion.hh.

References BLI_assert, from_rotation(), is_unit_scale(), and to_euler().

◆ to_gimbal_axis()

template<typename T>

MatBase< T, 3, 3 > blender::math::to_gimbal_axis ( const Euler3Base< T > & rotation )

nodiscard

Convert euler rotation to gimbal rotation matrix.

Definition at line 361 of file BLI_math_rotation.hh.

References from_rotation(), blender::math::Euler3Base< T >::i(), blender::math::Euler3Base< T >::i_index(), blender::math::Euler3Base< T >::j_index(), blender::math::Euler3Base< T >::k_index(), result, and T.

Referenced by blender::math::tests::TEST().

◆ to_loc_rot_scale() [1/2]

template<bool AllowNegativeScale = false, typename T>

void blender::math::to_loc_rot_scale	(	const MatBase< T, 3, 3 > &	mat,
		VecBase< T, 2 > &	r_location,
		AngleRadianBase< T > &	r_rotation,
		VecBase< T, 2 > &	r_scale )

inline

Definition at line 1362 of file BLI_math_matrix.hh.

References blender::MatBase< T, NumCol, NumRow, Alignment >::location(), and to_rot_scale().

Referenced by blender::nodes::node_composite_image_info_cc::ImageInfoOperation::execute(), interpolate_fast(), blender::eevee::IrradianceBake::surfel_raster_views_sync(), blender::tests::TEST(), blender::tests::TEST(), and to_loc_rot_scale_safe().

◆ to_loc_rot_scale() [2/2]

template<bool AllowNegativeScale = false, typename T, typename RotationT>

void blender::math::to_loc_rot_scale	(	const MatBase< T, 4, 4 > &	mat,
		VecBase< T, 3 > &	r_location,
		RotationT &	r_rotation,
		VecBase< T, 3 > &	r_scale )

inline

Definition at line 1387 of file BLI_math_matrix.hh.

References blender::MatBase< T, NumCol, NumRow, Alignment >::location(), and to_rot_scale().

◆ to_loc_rot_scale_safe()

template<bool AllowNegativeScale, typename T, typename RotationT>

void blender::math::to_loc_rot_scale_safe	(	const MatBase< T, 4, 4 > &	mat,
		VecBase< T, 3 > &	r_location,
		RotationT &	r_rotation,
		VecBase< T, 3 > &	r_scale )

inline

Same as to_loc_rot_scale but is handles matrices that are not only location, rotation and scale more gracefully, e.g. when the matrix has skew.

Definition at line 1401 of file BLI_math_matrix.hh.

References to_loc_rot_scale(), and to_quaternion().

Referenced by blender::bke::attribute_math::float4x4Mixer::mix_in(), blender::nodes::node_fn_combine_transform_cc::node_eval_inverse(), blender::nodes::node_geo_object_info_cc::node_geo_exec(), blender::ed::object::set_local_object_transform(), and blender::bke::greasepencil::Layer::set_local_transform().

◆ to_nearest_euler() [1/4]

template<typename T>

Euler3Base< T > blender::math::to_nearest_euler	(	const MatBase< T, 3, 3 > &	mat,
		const Euler3Base< T > &	reference )

inlinenodiscard

Definition at line 1222 of file BLI_math_matrix.hh.

References length_manhattan(), blender::math::detail::normalized_to_eul2(), blender::math::Euler3Base< T >::order(), and blender::math::Euler3Base< T >::wrapped_around().

◆ to_nearest_euler() [2/4]

template<typename T>

EulerXYZBase< T > blender::math::to_nearest_euler	(	const MatBase< T, 3, 3 > &	mat,
		const EulerXYZBase< T > &	reference )

inlinenodiscard

Extract euler rotation from transform matrix. The returned euler triple is given to be the closest from the reference. It avoids axis flipping for animated f-curves for eg.

Returns: the rotation with the smallest values from the potential candidates.

Note: this correspond to the C API "to_compatible" functions.

Definition at line 1237 of file BLI_math_matrix.hh.

References length_manhattan(), blender::math::detail::normalized_to_eul2(), and blender::math::EulerXYZBase< T >::wrapped_around().

Referenced by blender::tests::TEST().

◆ to_nearest_euler() [3/4]

template<typename T>

Euler3Base< T > blender::math::to_nearest_euler	(	const MatBase< T, 4, 4 > &	mat,
		const Euler3Base< T > &	reference )

inlinenodiscard

Definition at line 1252 of file BLI_math_matrix.hh.

References to_euler().

◆ to_nearest_euler() [4/4]

template<typename T>

EulerXYZBase< T > blender::math::to_nearest_euler	(	const MatBase< T, 4, 4 > &	mat,
		const EulerXYZBase< T > &	reference )

inlinenodiscard

Definition at line 1260 of file BLI_math_matrix.hh.

References to_euler().

◆ to_quaternion() [1/10]

template Quaternion blender::math::to_quaternion ( const AxisAngle & )

extern

◆ to_quaternion() [2/10]

template<typename T, typename AngleT>

QuaternionBase< T > blender::math::to_quaternion ( const AxisAngleBase< T, AngleT > & axis_angle )

Definition at line 71 of file BLI_math_axis_angle.hh.

References blender::math::AxisAngleBase< T, AngleT >::angle(), blender::math::AxisAngleBase< T, AngleT >::axis(), BLI_assert, cos(), is_unit_scale(), sin(), and T.

◆ to_quaternion() [3/10]

template Quaternion blender::math::to_quaternion ( const AxisAngleCartesian & )

extern

◆ to_quaternion() [4/10]

template<typename T>

QuaternionBase< T > blender::math::to_quaternion ( const CartesianBasis & rotation )

Creates a quaternion from an axis triple. This is faster and more precise than converting from another representation.

There are only 6 * 4 = 24 possible valid orthonormal orientations. We precompute them and store them inside this switch using a key. Generated using generate_axes_to_quaternion_switch_cases().

Definition at line 393 of file BLI_math_rotation.hh.

References blender::math::CartesianBasis::axes, blender::math::QuaternionBase< T >::identity(), rcp(), blender::math::numbers::sqrt2, T, x, blender::math::AxisSigned::X_NEG, blender::math::AxisSigned::X_POS, y, blender::math::AxisSigned::Y_NEG, blender::math::AxisSigned::Y_POS, z(), blender::math::AxisSigned::Z_NEG, and blender::math::AxisSigned::Z_POS.

◆ to_quaternion() [5/10]

template Quaternion blender::math::to_quaternion ( const Euler3 & )

extern

◆ to_quaternion() [6/10]

template<typename T>

QuaternionBase< T > blender::math::to_quaternion ( const Euler3Base< T > & eulO )

Definition at line 75 of file BLI_math_euler.hh.

References blender::math::Euler3Base< T >::i_index(), blender::math::Euler3Base< T >::ijk(), blender::math::Euler3Base< T >::j_index(), blender::math::Euler3Base< T >::k_index(), blender::math::Euler3Base< T >::parity(), to_quaternion(), UNPACK3, blender::math::QuaternionBase< T >::w, blender::math::QuaternionBase< T >::x, blender::math::EulerBase< T >::y(), blender::math::QuaternionBase< T >::y, and blender::math::QuaternionBase< T >::z.

◆ to_quaternion() [7/10]

template Quaternion blender::math::to_quaternion ( const EulerXYZ & )

extern

◆ to_quaternion() [8/10]

template<typename T>

QuaternionBase< T > blender::math::to_quaternion ( const EulerXYZBase< T > & eul )

Definition at line 50 of file BLI_math_euler.hh.

References cos(), sin(), T, blender::math::QuaternionBase< T >::w, blender::math::EulerBase< T >::x(), blender::math::QuaternionBase< T >::x, blender::math::EulerBase< T >::y(), blender::math::QuaternionBase< T >::y, blender::math::EulerBase< T >::z(), and blender::math::QuaternionBase< T >::z.

◆ to_quaternion() [9/10]

template<typename T>

QuaternionBase< T > blender::math::to_quaternion ( const MatBase< T, 3, 3 > & mat )

inlinenodiscard

Extract quaternion rotation from transform matrix.

Definition at line 1268 of file BLI_math_matrix.hh.

References blender::math::detail::normalized_to_quat_with_checks().

◆ to_quaternion() [10/10]

template<typename T>

QuaternionBase< T > blender::math::to_quaternion ( const MatBase< T, 4, 4 > & mat )

inlinenodiscard

Definition at line 1274 of file BLI_math_matrix.hh.

References to_quaternion().

◆ to_quaternion_legacy()

Quaternion blender::math::to_quaternion_legacy ( const float3x3 & mat )

nodiscard

Extract quaternion rotation from transform matrix. Legacy version of to_quaternion which has slightly different behavior. Keep for particle-system & boids since replacing this will make subtle changes that impact hair in existing files. See: D15772.

Definition at line 442 of file math_matrix.cc.

References atan2(), conjugate(), cos(), nor, normalize, safe_acos(), sin(), to_quaternion_legacy(), transform_point(), blender::MatBase< T, NumCol, NumRow, Alignment >::x_axis(), and blender::MatBase< T, NumCol, NumRow, Alignment >::z_axis().

Referenced by blender::tests::TEST(), and to_quaternion_legacy().

◆ to_rot_scale() [1/2]

template<bool AllowNegativeScale = false, typename T>

void blender::math::to_rot_scale	(	const MatBase< T, 2, 2 > &	mat,
		AngleRadianBase< T > &	r_rotation,
		VecBase< T, 2 > &	r_scale )

inline

Decompose a matrix into location, rotation, and scale components.

Template Parameters

AllowNegativeScale if true, will compute determinant to know if matrix is negative. Rotation and scale values will be flipped if it is negative. This is a costly operation so it is disabled by default.

Definition at line 1347 of file BLI_math_matrix.hh.

References is_negative(), normalize_and_get_size(), blender::math::detail::to_rotation(), and UNLIKELY.

Referenced by interpolate_fast(), blender::tests::TEST(), to_loc_rot_scale(), and to_loc_rot_scale().

◆ to_rot_scale() [2/2]

template<bool AllowNegativeScale = false, typename T, typename RotationT>

void blender::math::to_rot_scale	(	const MatBase< T, 3, 3 > &	mat,
		RotationT &	r_rotation,
		VecBase< T, 3 > &	r_scale )

inline

Definition at line 1372 of file BLI_math_matrix.hh.

References is_negative(), normalize_and_get_size(), blender::math::detail::to_rotation(), and UNLIKELY.

◆ to_scale() [1/2]

template<bool AllowNegativeScale = false, typename T>

VecBase< T, 2 > blender::math::to_scale ( const MatBase< T, 2, 2 > & mat )

inlinenodiscard

Definition at line 1306 of file BLI_math_matrix.hh.

References is_negative(), length(), result, and UNLIKELY.

◆ to_scale() [2/2]

template<bool AllowNegativeScale = false, typename T, int NumCol, int NumRow>

VecBase< T, 3 > blender::math::to_scale ( const MatBase< T, NumCol, NumRow > & mat )

inlinenodiscard

Extract the absolute 3d scale from a transform matrix.

Template Parameters

AllowNegativeScale if true, will compute determinant to know if matrix is negative. This is a costly operation so it is disabled by default.

Definition at line 1294 of file BLI_math_matrix.hh.

References is_negative(), length(), result, UNLIKELY, blender::MatBase< T, NumCol, NumRow, Alignment >::x_axis(), blender::MatBase< T, NumCol, NumRow, Alignment >::y_axis(), and blender::MatBase< T, NumCol, NumRow, Alignment >::z_axis().

Referenced by BKE_light_area(), boundbox_to_dimensions(), blender::nodes::node_fn_separate_transform_cc::SeparateTransformFunction::call(), blender::ed::greasepencil::create_curves_outline(), blender::io::usd::USDPointInstancerWriter::do_write(), blender::ed::greasepencil::image_render::draw_circles(), blender::generate_curves(), blender::ed::sculpt_paint::grease_pencil_fill_extension_lines_from_circles(), blender::eevee::IrradianceBake::init(), blender::bke::attribute_math::mix3(), blender::bke::attribute_math::mix4(), blender::draw::overlay::LightProbes::object_sync(), blender::workbench::VolumePass::object_sync_volume(), blender::io::grease_pencil::shape_attributes_to_curves(), blender::eevee::IrradianceBake::surfels_create(), ObjectInfos::sync(), blender::tests::TEST(), to_dual_quaternion(), and blender::ed::view3d::geometry_nodes_gizmos::DialGizmo::update_transform().

◆ to_vector() [1/2]

template<typename T>

T blender::math::to_vector ( const Axis axis )

Create basis vector.

Definition at line 322 of file BLI_math_basis_types.hh.

References blender::math::Axis::as_int(), BLI_assert, and T.

Referenced by blender::math::AxisAngleBase< T, AngleT >::AxisAngleBase(), blender::math::detail::from_rotation(), blender::ed::view3d::geometry_nodes_gizmos::TransformGizmos::get_axis_gizmo_matrix_basis(), blender::ed::view3d::geometry_nodes_gizmos::matrix_from_position_and_up_direction(), blender::tests::TEST(), blender::tests::TEST(), blender::tests::TEST(), blender::ed::view3d::geometry_nodes_gizmos::TransformGizmos::update_rotate_transform_and_target_property(), and blender::ed::view3d::geometry_nodes_gizmos::TransformGizmos::update_scale_transform_and_target_property().

◆ to_vector() [2/2]

template<typename T>

T blender::math::to_vector ( const AxisSigned axis )

Create signed basis vector.

Definition at line 331 of file BLI_math_basis_types.hh.

References abs, BLI_assert, blender::math::AxisSigned::from_int(), blender::math::AxisSigned::is_negative(), and T.

◆ transform_direction() [1/4]

template float3 blender::math::transform_direction	(	const float3x3 &	mat,
		const float3 &	direction )

extern

◆ transform_direction() [2/4]

template float3 blender::math::transform_direction	(	const float4x4 &	mat,
		const float3 &	direction )

extern

◆ transform_direction() [3/4]

template<typename T>

VecBase< T, 3 > blender::math::transform_direction	(	const MatBase< T, 3, 3 > &	mat,
		const VecBase< T, 3 > &	direction )

nodiscard

Transform a 3d direction vector using a 3x3 matrix (rotation & scale).

Definition at line 1653 of file BLI_math_matrix.hh.

◆ transform_direction() [4/4]

template<typename T>

VecBase< T, 3 > blender::math::transform_direction	(	const MatBase< T, 4, 4 > &	mat,
		const VecBase< T, 3 > &	direction )

nodiscard

Transform a 3d direction vector using a 4x4 matrix (rotation & scale).

Definition at line 1659 of file BLI_math_matrix.hh.

References view.

◆ transform_normals() [1/2]

void blender::math::transform_normals	(	const float3x3 &	transform,
		MutableSpan< float3 >	normals )

Transform normal vectors, maintaining their unit length status, but implementing some optimizations for identity matrix and uniform scaling.

Definition at line 552 of file math_matrix.cc.

References blender::MatBase< float, 3, 3 >::identity(), invert(), is_equal(), is_similarity_transform(), normalize(), normals, blender::threading::parallel_for(), transform(), transform_normals(), and transpose().

Referenced by blender::geometry::execute_realize_curve_task(), blender::ed::mesh::join_normals(), blender::bke::transform_custom_normal_attribute(), transform_normals(), transform_normals(), and blender::tests::transform_normals_test().

◆ transform_normals() [2/2]

void blender::math::transform_normals	(	Span< float3 >	src,
		const float3x3 &	transform,
		MutableSpan< float3 >	dst )

Definition at line 575 of file math_matrix.cc.

References blender::MutableSpan< T >::copy_from(), blender::MatBase< float, 3, 3 >::identity(), blender::Span< T >::index_range(), invert(), is_equal(), is_similarity_transform(), normalize(), blender::threading::parallel_for(), transform(), transform_normals(), and transpose().

◆ transform_point() [1/9]

template<typename T>

VecBase< T, 3 > blender::math::transform_point	(	const CartesianBasis &	basis,
		const VecBase< T, 3 > &	v )

inlinenodiscard

Definition at line 446 of file BLI_math_basis_types.hh.

References blender::math::Axis::as_int(), blender::math::AxisSigned::axis(), blender::math::AxisSigned::is_negative(), result, v, blender::math::CartesianBasis::x(), blender::math::CartesianBasis::y(), and blender::math::CartesianBasis::z().

◆ transform_point() [2/9]

template<typename T>

VecBase< T, 3 > blender::math::transform_point	(	const DualQuaternionBase< T > &	dq,
		const VecBase< T, 3 > &	point,
		MatBase< T, 3, 3 > *	r_crazy_space_mat = nullptr )

nodiscard

Transform point using the dual-quaternion dq . Applying the DualQuaternion transform can only happen if the DualQuaternion was normalized first. Optionally outputs crazy space matrix.

From: "Skinning with Dual Quaternions" Ladislav Kavan, Steven Collins, Jiri Zara, Carol O'Sullivan Trinity College Dublin, Czech Technical University in Prague

Definition at line 486 of file BLI_math_quaternion.hh.

References BLI_assert, is_normalized(), is_unit_scale(), M, blender::math::DualQuaternionBase< T >::quat, result, blender::math::DualQuaternionBase< T >::scale, blender::math::DualQuaternionBase< T >::scale_weight, T, blender::math::DualQuaternionBase< T >::trans, transform_point(), and view.

◆ transform_point() [3/9]

template float3 blender::math::transform_point	(	const float3x3 &	mat,
		const float3 &	point )

extern

◆ transform_point() [4/9]

template float3 blender::math::transform_point	(	const float4x4 &	mat,
		const float3 &	point )

extern

◆ transform_point() [5/9]

template<typename T>

VecBase< T, 2 > blender::math::transform_point	(	const MatBase< T, 2, 2 > &	mat,
		const VecBase< T, 2 > &	point )

nodiscard

Transform a 2d point using a 2x2 matrix (rotation & scale).

Definition at line 1629 of file BLI_math_matrix.hh.

◆ transform_point() [6/9]

template<typename T>

VecBase< T, 2 > blender::math::transform_point	(	const MatBase< T, 3, 3 > &	mat,
		const VecBase< T, 2 > &	point )

nodiscard

Transform a 2d point using a 3x3 matrix (location & rotation & scale).

Definition at line 1635 of file BLI_math_matrix.hh.

References blender::MatBase< T, NumCol, NumRow, Alignment >::location(), and view.

◆ transform_point() [7/9]

template<typename T>

VecBase< T, 3 > blender::math::transform_point	(	const MatBase< T, 3, 3 > &	mat,
		const VecBase< T, 3 > &	point )

nodiscard

Transform a 3d point using a 3x3 matrix (rotation & scale).

Definition at line 1641 of file BLI_math_matrix.hh.

◆ transform_point() [8/9]

template<typename T>

VecBase< T, 3 > blender::math::transform_point	(	const MatBase< T, 4, 4 > &	mat,
		const VecBase< T, 3 > &	point )

nodiscard

Transform a 3d point using a 4x4 matrix (location & rotation & scale).

Definition at line 1647 of file BLI_math_matrix.hh.

References blender::MatBase< T, NumCol, NumRow, Alignment >::location(), and view.

◆ transform_point() [9/9]

template<typename T>

VecBase< T, 3 > blender::math::transform_point	(	const QuaternionBase< T > &	q,
		const VecBase< T, 3 > &	v )

inlinenodiscard

Transform v by rotation using the quaternion q.

Definition at line 313 of file BLI_math_quaternion.hh.

References conjugate(), R, T, UNPACK3, V, v, blender::math::QuaternionBase< T >::w, blender::math::QuaternionBase< T >::x, blender::math::QuaternionBase< T >::y, and blender::math::QuaternionBase< T >::z.

◆ transform_points() [1/2]

void blender::math::transform_points	(	const float4x4 &	transform,
		MutableSpan< float3 >	points,
		bool	use_threading = true )

Transform point vectors with matrix multiplication, optionally using multi-threading.

Definition at line 640 of file math_matrix.cc.

References blender::MutableSpan< T >::index_range(), blender::threading::parallel_for(), skip_transform(), transform(), transform_points(), and transform_points_no_threading().

◆ transform_points() [2/2]

void blender::math::transform_points	(	Span< float3 >	src,
		const float4x4 &	transform,
		MutableSpan< float3 >	dst,
		bool	use_threading = true )

Definition at line 613 of file math_matrix.cc.

References blender::MutableSpan< T >::copy_from(), blender::Span< T >::index_range(), blender::threading::parallel_for(), skip_transform(), transform(), transform_points(), and transform_points_no_threading().

◆ transform_points_no_threading() [1/2]

void blender::math::transform_points_no_threading	(	const float4x4 &	transform,
		MutableSpan< float3 >	points )

static

Definition at line 633 of file math_matrix.cc.

References transform(), transform_point(), and transform_points_no_threading().

◆ transform_points_no_threading() [2/2]

void blender::math::transform_points_no_threading	(	const Span< float3 >	src,
		const float4x4 &	transform,
		MutableSpan< float3 >	dst )

static

Definition at line 604 of file math_matrix.cc.

References i, blender::Span< T >::index_range(), transform(), transform_point(), and transform_points_no_threading().

Referenced by transform_points(), transform_points(), transform_points_no_threading(), and transform_points_no_threading().

◆ translate()

template<typename T, int NumCol, int NumRow, typename VectorT>

MatBase< T, NumCol, NumRow > blender::math::translate	(	const MatBase< T, NumCol, NumRow > &	mat,
		const VectorT &	translation )

nodiscard

Equivalent to mat * from_location(translation) but with fewer operation.

Definition at line 659 of file BLI_math_matrix.hh.

References BLI_STATIC_ASSERT, result, and blender::unroll().

Referenced by blender::compositor::RealizeOnDomainOperation::execute(), blender::draw::overlay::Fluids::object_sync(), blender::draw::overlay::ForceFields::object_sync(), blender::ed::sculpt_paint::paint_cursor_drawing_setup_cursor_space(), blender::eevee::CaptureView::render_probes(), blender::ed::sculpt_paint::SCULPT_layer_brush_height_preview_draw(), and blender::tests::TEST().

◆ transpose()

template<typename T, int NumCol, int NumRow>

MatBase< T, NumCol, NumRow > blender::math::transpose ( const MatBase< T, NumRow, NumCol > & mat )

nodiscard

Flip the matrix across its diagonal. Also flips dimensions for non square matrices.

Definition at line 651 of file BLI_math_matrix.hh.

References i, result, and blender::unroll().

Referenced by blender::ed::greasepencil::calculate_texture_space(), blender::ed::transform::SnapData::clip_planes_enable(), blender::nodes::node_geo_scale_elements_cc::create_single_axis_transform(), blender::bke::CurvesSurfaceTransforms::CurvesSurfaceTransforms(), blender::ed::greasepencil::DrawingPlacement::DrawingPlacement(), blender::ed::spreadsheet::format_matrix_to_grid(), blender::get_legacy_stroke_matrix(), blender::ed::greasepencil::grease_pencil_texture_gradient_exec(), blender::nodes::node_fn_transpose_matrix_cc::node_build_multi_function(), blender::draw::sculpt_batches_get_ex(), blender::bke::greasepencil::Drawing::set_texture_matrices(), blender::eevee::VolumeProbeModule::set_view(), blender::eevee::ShadowTileMap::sync_cubeface(), blender::eevee::ShadowTileMap::sync_orthographic(), transform_normals(), transform_normals(), and blender::tests::transform_normals_test().

◆ vector_hash()

template<typename T>

uint64_t blender::math::vector_hash ( const T & vec )

Definition at line 46 of file BLI_math_vector_types.hh.

References BLI_STATIC_ASSERT, result, and T.

◆ whitepoint_from_temp_tint()

float3 blender::math::whitepoint_from_temp_tint	(	float	temperature,
		float	tint )

Definition at line 851 of file math_color.cc.

References clamp(), i, interpolate(), blender::math::locus_entry_t::mired, normalize, planck_locus, blender::math::locus_entry_t::t, blender::math::locus_entry_t::uv, x, and y.

Referenced by blender::ocio::calculate_white_point_matrix(), blender::nodes::node_composite_colorbalance_cc::get_white_point_matrix(), IMB_colormanagement_get_whitepoint(), and blender::nodes::node_composite_colorbalance_cc::white_point_variable().

◆ whitepoint_to_temp_tint()

bool blender::math::whitepoint_to_temp_tint	(	const float3 &	white,
		float &	temperature,
		float &	tint )

Definition at line 820 of file math_color.cc.

References blender::math::locus_entry_t::dist(), dot(), i, interpolate(), length(), blender::math::locus_entry_t::mired, planck_locus, sqrtf, blender::math::locus_entry_t::t, and blender::math::locus_entry_t::uv.

Referenced by IMB_colormanagement_set_whitepoint().

◆ wrap_coord()

BLI_INLINE int blender::math::wrap_coord	(	float	u,
		int	size,
		InterpWrapMode	wrap )

Definition at line 23 of file math_interp.cc.

References BLI_INLINE, Border, clamp(), Extend, floored_fmod(), Repeat, size(), wrap(), and x.

Referenced by bicubic_interpolation(), and interpolate_nearest_wrapmode_fl().

Variable Documentation

◆ is_math_float_type

template<typename T>

bool blender::math::is_math_float_type = std::is_floating_point_v<T>

inlineconstexpr

Definition at line 20 of file BLI_math_base.hh.

Referenced by blender::seq::gaussian_blur_x(), and blender::seq::gaussian_blur_y().

◆ is_math_integral_type

template<typename T>

bool blender::math::is_math_integral_type = std::is_integral_v<T>

inlineconstexpr

Definition at line 21 of file BLI_math_base.hh.

◆ planck_locus

const std::array<locus_entry_t, 31> blender::math::planck_locus

static

Initial value:

{{
    {0.0f, {0.18006f, 0.26352f}, -0.24341f},   {10.0f, {0.18066f, 0.26589f}, -0.25479f},
    {20.0f, {0.18133f, 0.26846f}, -0.26876f},  {30.0f, {0.18208f, 0.27119f}, -0.28539f},
    {40.0f, {0.18293f, 0.27407f}, -0.30470f},  {50.0f, {0.18388f, 0.27709f}, -0.32675f},
    {60.0f, {0.18494f, 0.28021f}, -0.35156f},  {70.0f, {0.18611f, 0.28342f}, -0.37915f},
    {80.0f, {0.18740f, 0.28668f}, -0.40955f},  {90.0f, {0.18880f, 0.28997f}, -0.44278f},
    {100.0f, {0.19032f, 0.29326f}, -0.47888f}, {125.0f, {0.19462f, 0.30141f}, -0.58204f},
    {150.0f, {0.19962f, 0.30921f}, -0.70471f}, {175.0f, {0.20525f, 0.31647f}, -0.84901f},
    {200.0f, {0.21142f, 0.32312f}, -1.0182f},  {225.0f, {0.21807f, 0.32909f}, -1.2168f},
    {250.0f, {0.22511f, 0.33439f}, -1.4512f},  {275.0f, {0.23247f, 0.33904f}, -1.7298f},
    {300.0f, {0.24010f, 0.34308f}, -2.0637f},  {325.0f, {0.24792f, 0.34655f}, -2.4681f},
    {350.0f, {0.25591f, 0.34951f}, -2.9641f},  {375.0f, {0.26400f, 0.35200f}, -3.5814f},
    {400.0f, {0.27218f, 0.35407f}, -4.3633f},  {425.0f, {0.28039f, 0.35577f}, -5.3762f},
    {450.0f, {0.28863f, 0.35714f}, -6.7262f},  {475.0f, {0.29685f, 0.35823f}, -8.5955f},
    {500.0f, {0.30505f, 0.35907f}, -11.324f},  {525.0f, {0.31320f, 0.35968f}, -15.628f},
    {550.0f, {0.32129f, 0.36011f}, -23.325f},  {575.0f, {0.32931f, 0.36038f}, -40.770f},
    {600.0f, {0.33724f, 0.36051f}, -116.45f},
}}

Definition at line 801 of file math_color.cc.

Referenced by whitepoint_from_temp_tint(), and whitepoint_to_temp_tint().

Namespaces

Classes

Typedefs

Enumerations

Functions

Variables

Typedef Documentation

◆ AngleCartesian

◆ AngleRadian

◆ AxisAngle

◆ AxisAngleCartesian

◆ DualQuaternion

◆ Euler3

◆ EulerXYZ

◆ Quaternion

Enumeration Type Documentation

◆ eCubicFilter

◆ EulerOrder

◆ InterpWrapMode

Function Documentation

◆ abs() [1/3]

◆ abs() [2/3]

◆ abs() [3/3]

◆ acos()

◆ adjoint() [1/7]

◆ adjoint() [2/7]

◆ adjoint() [3/7]

◆ adjoint() [4/7]

◆ adjoint() [5/7]

◆ adjoint() [6/7]

◆ adjoint() [7/7]

◆ almost_equal_relative()

◆ angle_between() [1/3]

◆ angle_between() [2/3]

◆ angle_between() [3/3]

◆ angle_between_signed()

◆ angle_of()

◆ angle_of_signed()

◆ asin()

◆ atan()

◆ atan2()

◆ average()

◆ bicubic_interpolation()

◆ bilinear_byte_impl()

◆ bilinear_fl_impl()

◆ canonicalize()

◆ ceil() [1/2]

◆ ceil() [2/2]

◆ ceil_to_multiple()

◆ chromatic_adaption_matrix()

◆ clamp() [1/3]

◆ clamp() [2/3]

◆ clamp() [3/3]

◆ conjugate()

◆ cos() [1/4]

◆ cos() [2/4]

◆ cos() [3/4]

◆ cos() [4/4]

◆ cross() [1/3]

◆ cross() [2/3]

◆ cross() [3/3]

◆ cross_high_precision()

◆ cross_poly()

◆ cross_tri()

◆ cube()

◆ cubic_filter_coefficients()

◆ determinant() [1/7]

◆ determinant() [2/7]

◆ determinant() [3/7]

◆ determinant() [4/7]

◆ determinant() [5/7]

◆ determinant() [6/7]

◆ determinant() [7/7]

◆ distance() [1/2]

◆ distance() [2/2]

◆ distance_manhattan()

◆ distance_squared()

◆ divide_ceil()

◆ dominant_axis()

◆ dot() [1/2]